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1.

図書
図書
1. Fourier integrals in classical analysis. 2nd ed (: hardback)
Christopher D. Sogge
出版情報: Cambridge : Cambridge University Press, 2017  xiv, 334 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 210
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2.

図書
図書
2. A primer on Fourier analysis for the geosciences (: pbk)
Robin Crockett
出版情報: Cambridge : Cambridge University Press, 2019  xiv, 176 p. ; 23 cm
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3.

図書
図書
3. Theory of function spaces ([1] - 3)
Hans Triebel
出版情報: Basel ; Boston : Birkhäuser Verlag, c1983-  v. ; 24 cm
シリーズ名: Monographs in mathematics ; v. 78, 84, 100
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目次情報: 続きを見る
Preface
How to Measure Smoothness / 1：
Atoms and Pointwise Multipliers / 2：
Wavelets / 3：
Spaces on Domains, Wavelets, Sampling Numbers / 4：
Anisotropic Function Spaces / 5：
Weighted Function Spaces / 6：
Fractal Analysis / 7：
Function Spaces on Quasi-metric Spaces / 8：
Function Spaces on Sets / 9：
References
Notation, Symbols
Index
Preface
How to Measure Smoothness / 1：
Atoms and Pointwise Multipliers / 2：
4.

図書
図書
4. Algebraic numbers and Fourier analysis . Selected problems on exceptional sets
Raphaël Salem . Lennart Carleson
出版情報: Belmont, Calif. : Wadsworth International Group, c1983  66, iii, 98 p. ; 25 cm
シリーズ名: The Wadsworth mathematics series
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5.

図書
図書
5. Topics in Fourier analysis and function spaces
Hans-Jürgen Schmeisser, Hans Triebel
出版情報: Chichester ; New York : Wiley, c1987  300 p. ; 24 cm
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6.

図書
図書
6. A handbook of Fourier theorems (: hard ; : pbk)
D. C. Champeney
出版情報: Cambridge : Cambridge University Press, 1987  ix, 185 p. ; 24 cm
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目次情報: 続きを見る
Preface
Introduction / 1：
Lebesgue integration / 2：
Riemann integration / 2.1：
Null sets / 2.3：
The Lebesgue integral / 2.4：
Nomenclature / 2.5：
Conditions for integrability; measurability / 2.6：
Functions in L[[superscript p]] / 2.7：
Integrals in several dimensions / 2.8：
Alternative approaches / 2.9：
Some useful theorems / 3：
The Minkowski inequality / 3.1：
Holder's theorem / 3.2：
Young's theorem / 3.3：
The Fubini and Tonelli theorems / 3.4：
Two theorems of Lebesgue / 3.5：
Absolute and uniform continuity / 3.6：
The Riemann--Lebesgue theorem / 3.7：
Convergence of sequences of functions / 4：
Pointwise convergence / 4.1：
Bounded, dominated and monotone convergence / 4.3：
Uniform convergence / 4.4：
Convergence in the mean / 4.5：
Cauchy sequences / 4.6：
Local averages and convolution kernels / 5：
Lebesgue points / 5.1：
Approximate convolution identities / 5.3：
The Dirichlet kernel and Dirichlet points / 5.4：
The functions of du Bois-Reymond and of Fejer / 5.5：
Carleson's theorem / 5.6：
Kolmogoroff's theorem / 5.7：
The Dirichlet conditions / 5.8：
Jordan's theorem / 5.9：
Dini's theorem / 5.10：
The de la Vallee-Poussin test / 5.11：
Some general remarks on Fourier transformation / 6：
The definition of the Fourier transform / 6.1：
Sufficient conditions for transformability / 6.3：
Necessary conditions for transformability / 6.4：
Fourier theorems for good functions / 7：
Inversion, differentiation and convolution theorems / 7.1：
Good functions of bounded support / 7.3：
Fourier theorems in L[[superscript p]] / 8：
Basic theorems and definitions / 8.1：
More inversion theorems in L[[superscript p]] / 8.2：
Convolution and product theorems in L[[superscript p]] / 8.3：
Uncertainty principle and bandwidth theorem / 8.4：
The sampling theorem / 8.5：
Hilbert transforms and causal functions / 8.6：
Fourier theorems for functions outside L[[superscript p]] / 9：
Functions in class K / 9.1：
Convolutions and products in K / 9.3：
Functions outside K / 9.4：
Miscellaneous theorems / 10：
Differentiation and integration / 10.1：
The Gibbs phenomenon / 10.2：
Complex Fourier transforms / 10.3：
Positive-definite and distribution functions / 10.4：
Power spectra and Wiener's theorems / 11：
The autocorrelation function / 11.1：
The spectrum and spectral density / 11.3：
Discrete spectra / 11.4：
Continuous spectra / 11.5：
Generalized functions / 11.6：
The definition of functionals in S' / 12.1：
Basic theorems / 12.3：
Examples of generalized functions / 12.4：
Fourier transformation of generalized functions I / 13：
Definition of the transform / 13.1：
Simple properties of the transform / 13.2：
Examples of Fourier transforms / 13.3：
The convolution and product of functionals / 13.4：
Fourier transformation of generalized functions II / 14：
Functionals of types D' and Z' / 14.1：
Fourier transformation of functionals in D' / 14.2：
Transformation of products and convolutions in D' / 14.3：
Fourier series / 15：
Fourier coefficients of a periodic function / 15.1：
The convergence of Fourier series / 15.2：
Summability of Fourier series / 15.3：
Mean convergence of Fourier series / 15.4：
Sampling theorems / 15.5：
Differentiation and integration of Fourier series / 15.6：
Products and convolutions / 15.7：
Generalized Fourier series / 16：
Generalized Fourier coefficients / 16.1：
The Fourier formulae / 16.3：
Differentiation, repetition and sampling / 16.4：
Bibliography / 16.5：
Index
Preface
Introduction / 1：
Lebesgue integration / 2：
7.

図書
図書
7. Fourier and wavelet analysis
George Bachman, Lawrence Narici, Edward Beckenstein
出版情報: New York : Springer, c2000  ix, 505 p. ; 25 cm
シリーズ名: Universitext
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8.

図書
図書
8. Fourier analysis on finite groups and applications (: hbk ; : pbk)
Audrey Terras
出版情報: Cambridge, U.K. : Cambridge University Press, 1999  x, 442 p. ; 23 cm
シリーズ名: London Mathematical Society student texts ; 43
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目次情報: 続きを見る
Introduction
Cast of characters
Congruences and the quotient ring of the integers mod n / Part I：
The discrete Fourier transform on the finite circle / 1.2：
Graphs of Z/nZ, adjacency operators, eigenvalues / 1.3：
Four questions about Cayley graphs / 1.4：
Finite Euclidean graphs and three questions about their spectra / 1.5：
Random walks on Cayley graphs / 1.6：
Applications in geometry and analysis / 1.7：
The quadratic reciprocity law / 1.8：
The fast Fourier transform / 1.9：
The DFT on finite Abelian groups - finite tori / 1.10：
Error-correcting codes / 1.11：
The Poisson sum formula on a finite Abelian group / 1.12：
Some applications in chemistry and physics / 1.13：
The uncertainty principle / 1.14：
Fourier transform and representations of finite groups / Part II：
Induced representations / 2.2：
The finite ax + b group / 2.3：
Heisenberg group / 2.4：
Finite symmetric spaces - finite upper half planes Hq / 2.5：
Special functions on Hq - K-Bessel and spherical / 2.6：
The general linear group GL(2, Fq) / 2.7：
Selberg's trace formula and isospectral non-isomorphic graphs / 2.8：
The trace formula on finite upper half planes / 2.9：
The trace formula for a tree and Ihara's zeta function / 2.10：
Introduction
Cast of characters
Congruences and the quotient ring of the integers mod n / Part I：
9.

図書
図書
9. The Gibbs phenomenon in Fourier analysis, splines and wavelet approximations
by Abdul J. Jerri
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1998  xxvii, 336 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 446
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10.

図書
図書
10. Weyl transforms
M.W. Wong
出版情報: New York : Springer, c1998  viii, 158 p. ; 24 cm
シリーズ名: Universitext
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11.

図書
図書
11. Signals, sound, and sensation
William M. Hartmann
出版情報: Woodbury, N.Y. : American Institute of Physics, c1997  xvii, 647 p. ; 25 cm
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12.

図書
図書
12. Fourier analysis and boundary value problems
Enrique A. González-Velasco
出版情報: San Diego, CA ; Tokyo : Academic Press, c1995  xi, 551 p. ; 24 cm
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A Heated Discussion
Fourier Series
Return to the Heated Bar
Generalized Fourier Series
The Wave Equation
Orthogonal Systems
Fourier Transforms
Laplace Transforms
Boundary Value Problems in Higher Dimensions
Boundary Value Problems with Circular Symmetry
Boundary Value Problems with Spherical Symmetry
Uniform Convergence
Improper Integrals
Tables of Fourier and Laplace Transforms
Historical Bibliography
Index
A Heated Discussion
Fourier Series
Return to the Heated Bar
13.

図書
図書
13. Integration and probability
Paul Malliavin ; in cooperation with Hélène Airault, Leslie Kay, Gérard Letac
出版情報: New York ; Tokyo : Springer-Verlag, c1995  xxi, 322 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 157
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14.

図書
図書
14. Sampling theory in Fourier and signal analysis : foundations
J.R. Higgins
出版情報: Oxford : Clarendon Press, 1996  xiii, 222 p. ; 25 cm
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目次情報: 続きを見る
An introduction to sampling theory / 1：
General introduction / 1.1：
Introduction - continued / 1.2：
The seventeenth to the mid twentieth century - a brief review / 1.3：
Interpolation and sampling from the seventeenth century to the mid twentieth century - a brief review / 1.4：
Introduction - concluding remarks / 1.5：
Background in Fourier analysis / 2：
The Fourier Series / 2.1：
The Fourier transform / 2.2：
Poisson's summation formula / 2.3：
Tempered distributions - some basic facts / 2.4：
Hilbert spaces, bases and frames / 3：
Bases for Banach and Hilbert spaces / 3.1：
Riesz bases and unconditional bases / 3.2：
Frames / 3.3：
Reproducing kernel Hilbert spaces / 3.4：
Direct sums of Hilbert spaces / 3.5：
Sampling and reproducing kernels / 3.6：
Finite sampling / 4：
A general setting for finite sampling / 4.1：
Sampling on the sphere / 4.2：
From finite to infinite sampling series / 5：
The change to infinite sampling series / 5.1：
The Theorem of Hinsen and Kloosters / 5.2：
Bernstein and Paley-Weiner spaces / 6：
Convolution and the cardinal series / 6.1：
Sampling and entire functions of polynomial growth / 6.2：
Paley-Weiner spaces / 6.3：
The cardinal series for Paley-Weiner spaces / 6.4：
The space ReH1 / 6.5：
The ordinary Paley-Weiner space and its reproducing kernel / 6.6：
A convergence principle for general Paley-Weiner spaces / 6.7：
More about Paley-Weiner spaces / 7：
Paley-Weiner theorems - a review / 7.1：
Bases for Paley-Weiner spaces / 7.2：
Operators on the Paley-Weiner space / 7.3：
Oscillatory properties of Paley-Weiner functions / 7.4：
Kramer's lemma / 8：
Kramer's Lemma / 8.1：
The Walsh sampling therem / 8.2：
Contour integral methods / 9：
The Paley-Weiner theorem / 9.1：
Some formulae of analysis and their equivalence / 9.2：
A general sampling theorem / 9.3：
Irregular sampling / 10：
Sets of stable sampling, of interpolation and of uniqueness / 10.1：
Irregular sampling at minimal rate / 10.2：
Frames and over-sampling / 10.3：
Errors and aliasing / 11：
Errors / 11.1：
The time jitter error / 11.2：
The aliasing error / 11.3：
Multi-channel sampling / 12：
Single channel sampling / 12.1：
Two channels / 12.3：
Multi-band sampling / 13：
Regular sampling / 13.1：
Optimal regular sampling / 13.2：
An algorithm for the optimal regular sampling rate / 13.3：
Selectively tiled band regions / 13.4：
Harmonic signals / 13.5：
Band-ass sampling / 13.6：
Multi-dimensional sampling / 14：
Remarks on multi-dimensional Fourier analysis / 14.1：
The rectangular case / 14.2：
Regular multi-dimensional sampling / 14.3：
Sampling and eigenvalue problems / 15：
Preliminary facts / 15.1：
Direct and inverse Sturm-Liouville problems / 15.2：
Further types of eigenvalue problem - some examples / 15.3：
Campbell's generalised sampling theorem / 16：
L.L. Campbell's generalisation of the sampling theorem / 16.1：
Band-limited functions / 16.2：
Non band-limited functions - an example / 16.3：
Modelling, uncertainty and stable sampling / 17：
Remarks on signal modelling / 17.1：
Energy concentration / 17.2：
Prolate Spheroidal Wave functions / 17.3：
The uncertainty principle of signal theory / 17.4：
The Nyquist-Landau minimal sampling rate / 17.5：
An introduction to sampling theory / 1：
General introduction / 1.1：
Introduction - continued / 1.2：
15.

図書
図書
15. Fourier analysis of time series : an introduction
Peter Bloomfield
出版情報: New York : Wiley, c1976  xiii, 258 p. ; 24 cm
シリーズ名: Wiley series in probability and mathematical statistics ; . Applied probability and statistics
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目次情報: 続きを見る
Introduction / 1：
Fourier Analysis / 1.1：
Historical Development of Fourier Methods / 1.2：
Why Use Trigonometric Functions? / 1.3：
Fitting Sinusoids / 2：
Curve-Fitting Approach / 2.1：
Least Squares Fitting of Sinusoids / 2.2：
Multiple Periodicities / 2.3：
Orthogonality of Sinusoids / 2.4：
Effect of Discrete Time: Aliasing / 2.5：
Some Statistical Results / 2.6：
Appendix
The Search for Periodicity / 3：
Fitting the Frequency / 3.1：
Fitting Multiple Frequencies / 3.2：
Some More Statistical Results / 3.3：
Harmonic Analysis / 4：
Fourier Frequencies / 4.1：
Discrete Fourier Transform / 4.2：
Decomposing the Sum of Squares / 4.3：
Special Functions / 4.4：
Smooth Functions / 4.5：
The Fast Fourier Transform / 5：
Computational Cost of Fourier Transforms / 5.1：
Two-Factor Case / 5.2：
Application to Harmonic Analysis of Data / 5.3：
Examples of Harmonic Analysis / 6：
Variable Star Data / 6.1：
Leakage Reduction by Data Windows / 6.2：
Tapering the Variable Star Data / 6.3：
Wolf's Sunspot Numbers / 6.4：
Nonsinusoidal Oscillations / 6.5：
Amplitude and Phase Fluctuations / 6.6：
Transformations / 6.7：
Periodogram of a Noise Series / 6.8：
Fisher's Test for Periodicity / 6.9：
Complex Demodulation / 7：
Smoothing: Linear Filtering / 7.1：
Designing a Filter / 7.3：
Least Squares Filter Design / 7.4：
Demodulating the Sunspot Series / 7.5：
Complex Time Series / 7.6：
Sunspots: The Complex Series / 7.7：
The Spectrum / 8：
Periodogram Analysis of Wheat Prices / 8.1：
Analysis of Segments of a Series / 8.2：
Smoothing the Periodogram / 8.3：
Autocovariances and Spectrum Estimates / 8.4：
Alternative Representations / 8.5：
Choice of a Spectral Window / 8.6：
Examples of Smoothing the Periodogram / 8.7：
Reroughing the Spectrum / 8.8：
Some Stationary Time Series Theory / 9：
Stationary Time Series / 9.1：
Continuous Spectra / 9.2：
Time Averaging and Ensemble Averaging / 9.3：
Periodogram and Continuous Spectra / 9.4：
Approximate Mean and Variance / 9.5：
Properties of Spectral Windows / 9.6：
Aliasing and the Spectrum / 9.7：
Analysis of Multiple Series / 10：
Cross Periodogram / 10.1：
Estimating the Cross Spectrum / 10.2：
Theoretical Cross Spectrum / 10.3：
Distribution of the Cross Periodogram / 10.4：
Distribution of Estimated Cross Spectra / 10.5：
Alignment / 10.6：
Further Topics / 11：
Time Domain Analysis / 11.1：
Spatial Series / 11.2：
Multiple Series / 11.3：
Higher Order Spectra / 11.4：
Nonquadratic Spectrum Estimates / 11.5：
Incomplete and Irregular Data / 11.6：
References
Author Index
Subject Index
Introduction / 1：
Fourier Analysis / 1.1：
Historical Development of Fourier Methods / 1.2：
16.

図書
図書
16. The FFT, fundamentals and concepts
Robert W. Ramirez
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, c1985  xi, 178 p. ; 25 cm
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17.

図書
図書
17. Contributions to Fourier analysis
A. Zygmund ... [et al.]
出版情報: Princeton : Princeton University Press, 1950  v, 188 p. ; 26 cm
シリーズ名: Annals of mathematics studies ; no. 25
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18.

図書
図書
18. Fourier analysis and its applications
Gerald B. Folland
出版情報: Pacific Grove, Calif. : Wadsworth & Brooks/Cole Advanced Books & Software, c1992  x, 433 p. ; 24 cm
シリーズ名: The Wadsworth & Brooks/Cole mathematics series
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19.

図書
図書
19. Ondelettes
Yves Meyer
出版情報: Paris : Hermann, c1990  xii, 215 p. ; 24 cm
シリーズ名: Ondelettes et opérateurs ; 1
Actualités mathématiques
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20.

図書
図書
20. Walsh series : an introduction to dyadic harmonic analysis
F. Schipp, W.R. Wade, P. Simon
出版情報: Bristol ; New York : Adam Hilger, c1990  x, 560 p. ; 25 cm
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21.

図書
図書
21. Fourier analysis
James S. Walker
出版情報: New York : Oxford University Press, 1988  xix, 440 p. ; 24 cm
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目次情報: 続きを見る
Introduction to Fourier Series
Convergence of Fourier Series
Applications of Fourier Series
Some harmonic function theory
Multiple Fourier Series
Basic theory of the Fourier transform
Applications of Fourier transforms: 1) Partial differential equations; 2) Fourier optics
Legendre polynomials and spherical harmonics
Some other transforms: 1) The Laplace transform; 2) The Radon transform
A brief introduction to Bessel functions: A) Divergence of Fourier Series; B) Brief tables of Fourier Series and integrals
Introduction to Fourier Series
Convergence of Fourier Series
Applications of Fourier Series
22.

図書
図書
22. Theory of discrete and continuous Fourier analysis
H. Joseph Weaver
出版情報: New York : Wiley, c1989  xii, 307 p. ; 24 cm
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Basic Mathematical Background
Integration Theory
Distribution Theory
The Fourier Series
The Fourier Transform
Fourier Transform of a Distribution
The Discrete Fourier Transform
Sampling Theory
Appendix
Index
Basic Mathematical Background
Integration Theory
Distribution Theory
23.

図書
図書
23. Extreme eigen values of Toeplitz operators (: Berlin ; : New York)
I.I. Hirschman, Jr., Daniel Hughes
出版情報: Berlin ; New York : Springer-Verlag, 1977  145 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 618
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24.

図書
図書
24. Theory and applications of Fourier analysis
Charles Sparks Rees, S.M. Shah, Č.V. Stanojević
出版情報: New York : M. Dekker, c1981  viii, 419 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 59
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25.

図書
図書
25. Littlewood-Paley and multiplier theory (: gw ; : us)
R.E. Edwards, G.I. Gaudry
出版情報: Berlin ; New york : Springer-Verlag, 1977  ix, 212 p. ; 25 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 90
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26.

図書
図書
26. Chebyshev & Fourier spectral methods (: Berlin ; : New York)
J.P. Boyd
出版情報: Berlin ; Tokyo : Springer-Verlag, c1989  xvi, 798 p. ; 25 cm
シリーズ名: Lecture notes in engineering ; 49
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27.

図書
図書
27. Fourier analysis (: pbk)
T.W. Körner
出版情報: Cambridge [Cambridgeshire] : Cambridge University Press, 1988  xii, 591 p. ; 26 cm
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目次情報: 続きを見る
Preface
Fourier series / 1：
Some differential equations / 2：
Orthogonal series / 3：
Fourier transforms / 4：
Further developments / 5：
Other directions / 6：
Appendices
Index
Preface
Fourier series / 1：
Some differential equations / 2：
28.

図書
図書
28. A guide to distribution theory and Fourier transforms
Robert S. Strichartz
出版情報: Boca Raton : CRC Press, c1994  ix, 213 p. ; 25 cm
シリーズ名: Studies in advanced mathematics
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29.

図書
図書
29. Martingale Hardy spaces and their applications in Fourier analysis (: us ; : gw)
Ferenc Weisz
出版情報: Berlin ; New York : Springer-Verlag, c1994  viii, 217 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1568
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30.

図書
図書
30. Clifford wavelets, singular integrals, and Hardy spaces (: us ; : gw)
Marius Mitrea
出版情報: Berlin ; New York : Springer-Verlag, c1994  xi, 116 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1575
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31.

図書
図書
31. Introduction to Fourier analysis and wavelets
Mark A. Pinsky
出版情報: Australia : Brooks/Cole, c2002  xviii, 376 p. ; 25 cm
シリーズ名: Brooks/Cole series in advanced mathematics
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目次情報: 続きを見る
Fourier Series on the Circle / 1：
Motivation and Heuristics / 1.1：
Motivation from Physics / 1.1.1：
The Vibrating String / 1.1.1.1：
Heat Flow in Solids / 1.1.1.2：
Absolutely Convergent Trigonometric Series / 1.1.2：
Examples of Factorial and Bessel Functions / 1.1.3：
Poisson Kernel Example / 1.1.4：
Proof of Laplace's Method / 1.1.5：
Nonabsolutely Convergent Trigonometric Series / 1.1.6：
Formulation of Fourier Series / 1.2：
Fourier Coefficients and Their Basic Properties / 1.2.1：
Fourier Series of Finite Measures / 1.2.2：
Rates of Decay of Fourier Coefficients / 1.2.3：
Piecewise Smooth Functions / 1.2.3.1：
Fourier Characterization of Analytic Functions / 1.2.3.2：
Sine Integral / 1.2.4：
Other Proofs That Si([infinity]) = 1 / 1.2.4.1：
Pointwise Convergence Criteria / 1.2.5：
Integration of Fourier Series / 1.2.6：
Convergence of Fourier Series of Measures / 1.2.6.1：
Riemann Localization Principle / 1.2.7：
Gibbs-Wilbraham Phenomenon / 1.2.8：
The General Case / 1.2.8.1：
Fourier Series in L[superscript 2] / 1.3：
Mean Square Approximation--Parseval's Theorem / 1.3.1：
Application to the Isoperimetric Inequality / 1.3.2：
Rates of Convergence in L[superscript 2] / 1.3.3：
Application to Absolutely-Convergent Fourier Series / 1.3.3.1：
Norm Convergence and Summability / 1.4：
Approximate Identities / 1.4.1：
Almost-Everywhere Convergence of the Abel Means / 1.4.1.1：
Summability Matrices / 1.4.2：
Fejer Means of a Fourier Series / 1.4.3：
Wiener's Closure Theorem on the Circle / 1.4.3.1：
Equidistribution Modulo One / 1.4.4：
Hardy's Tauberian Theorem / 1.4.5：
Improved Trigonometric Approximation / 1.5：
Rates of Convergence in C (T) / 1.5.1：
Approximation with Fejer Means / 1.5.2：
Jackson's Theorem / 1.5.3：
Higher-Order Approximation / 1.5.4：
Converse Theorems of Bernstein / 1.5.5：
Divergence of Fourier Series / 1.6：
The Example of du Bois-Reymond / 1.6.1：
Analysis via Lebesgue Constants / 1.6.2：
Divergence in the Space L[superscript 1] / 1.6.3：
Appendix: Complements on Laplace's Method / 1.7：
First Variation on the Theme-Gaussian Approximation / 1.7.0.1：
Second Variation on the Theme-Improved Error Estimate / 1.7.0.2：
Application to Bessel Functions / 1.7.1：
The Local Limit Theorem of DeMoivre-Laplace / 1.7.2：
Appendix: Proof of the Uniform Boundedness Theorem / 1.8：
Appendix: Higher-Order Bessel functions / 1.9：
Appendix: Cantor's Uniqueness Theorem / 1.10：
Fourier Transforms on the Line And Space / 2：
Basic Properties of the Fourier Transform / 2.1：
Riemann-Lebesgue Lemma / 2.2.1：
Approximate Identities and Gaussian Summability / 2.2.2：
Improved Approximate Identities for Pointwise Convergence / 2.2.2.1：
Application to the Fourier Transform / 2.2.2.2：
The n-Dimensional Poisson Kernel / 2.2.2.3：
Fourier Transforms of Tempered Distributions / 2.2.3：
Characterization of the Gaussian Density / 2.2.4：
Wiener's Density Theorem / 2.2.5：
Fourier Inversion in One Dimension / 2.3：
Dirichlet Kernel and Symmetric Partial Sums / 2.3.1：
Example of the Indicator Function / 2.3.2：
Dini Convergence Theorem / 2.3.3：
Extension to Fourier's Single Integral / 2.3.4.1：
Smoothing Operations in R[superscript 1]-Averaging and Summability / 2.3.5：
Averaging and Weak Convergence / 2.3.6：
Cesaro Summability / 2.3.7：
Approximation Properties of the Fejer Kernel / 2.3.7.1：
Bernstein's Inequality / 2.3.8：
One-Sided Fourier Integral Representation / 2.3.9：
Fourier Cosine Transform / 2.3.9.1：
Fourier Sine Transform / 2.3.9.2：
Generalized h-Transform / 2.3.9.3：
L[superscript 2] Theory in R[superscript n] / 2.4：
Plancherel's Theorem / 2.4.1：
Bernstein's Theorem for Fourier Transforms / 2.4.2：
The Uncertainty Principle / 2.4.3：
Uncertainty Principle on the Circle / 2.4.3.1：
Spectral Analysis of the Fourier Transform / 2.4.4：
Hermite Polynomials / 2.4.4.1：
Eigenfunction of the Fourier Transform / 2.4.4.2：
Orthogonality Properties / 2.4.4.3：
Completeness / 2.4.4.4：
Spherical Fourier Inversion in R[superscript n] / 2.5：
Bochner's Approach / 2.5.1：
Piecewise Smooth Viewpoint / 2.5.2：
Relations with the Wave Equation / 2.5.3：
The Method of Brandolini and Colzani / 2.5.3.1：
Bochner-Riesz Summability / 2.5.4：
A General Theorem on Almost-Everywhere Summability / 2.5.4.1：
Bessel Functions / 2.6：
Fourier Transforms of Radial Functions / 2.6.1：
L[superscript 2]-Restriction Theorems for the Fourier Transform / 2.6.2：
An Improved Result / 2.6.2.1：
Limitations on the Range of p / 2.6.2.2：
The Method of Stationary Phase / 2.7：
Statement of the Result / 2.7.1：
Proof of the Method of Stationary Phase / 2.7.2：
Abel's Lemma / 2.7.4：
Fourier Analysis in L[superscript p] Spaces / 3：
The M. Riesz-Thorin Interpolation Theorem / 3.1：
Generalized Young's Inequality / 3.2.0.1：
The Hausdorff-Young Inequality / 3.2.0.2：
Stein's Complex Interpolation Theorem / 3.2.1：
The Conjugate Function or Discrete Hilbert Transform / 3.3：
L[superscript p] Theory of the Conjugate Function / 3.3.1：
L[superscript 1] Theory of the Conjugate Function / 3.3.2：
Identification as a Singular Integral / 3.3.2.1：
The Hilbert Transform on R / 3.4：
L[superscript 2] Theory of the Hilbert Transform / 3.4.1：
L[superscript p] Theory of the Hilbert Transform, 1 [ p [ [infinity] / 3.4.2：
Applications to Convergence of Fourier Integrals / 3.4.2.1：
L[superscript 1] Theory of the Hilbert Transform and Extensions / 3.4.3：
Kolmogorov's Inequality for the Hilbert Transform / 3.4.3.1：
Application to Singular Integrals with Odd Kernels / 3.4.4：
Hardy-Littlewood Maximal Function / 3.5：
Application to the Lebesgue Differentiation Theorem / 3.5.1：
Application to Radial Convolution Operators / 3.5.2：
Maximal Inequalities for Spherical Averages / 3.5.3：
The Marcinkiewicz Interpolation Theorem / 3.6：
Calderon-Zygmund Decomposition / 3.7：
A Class of Singular Integrals / 3.8：
Properties of Harmonic Functions / 3.9：
General Properties / 3.9.1：
Representation Theorems in the Disk / 3.9.2：
Representation Theorems in the Upper Half-Plane / 3.9.3：
Herglotz/Bochner Theorems and Positive Definite Functions / 3.9.4：
Poisson Summation Formula And Multiple Fourier Series / 4：
The Poisson Summation Formula in R[superscript 1] / 4.1：
Periodization of a Function / 4.2.1：
Statement and Proof / 4.2.2：
Shannon Sampling / 4.2.3：
Multiple Fourier Series / 4.3：
Basic L[superscript 1] Theory / 4.3.1：
Pointwise Convergence for Smooth Functions / 4.3.1.1：
Representation of Spherical Partial Sums / 4.3.1.2：
Basic L[superscript 2] Theory / 4.3.2：
Restriction Theorems for Fourier Coefficients / 4.3.3：
Poisson Summation Formula in R[superscript d] / 4.4：
Simultaneous Nonlocalization / 4.4.1：
Application to Lattice Points / 4.5：
Kendall's Mean Square Error / 4.5.1：
Landau's Asymptotic Formula / 4.5.2：
Application to Multiple Fourier Series / 4.5.3：
Three-Dimensional Case / 4.5.3.1：
Higher-Dimensional Case / 4.5.3.2：
Schrodinger Equation and Gauss Sums / 4.6：
Distributions on the Circle / 4.6.1：
The Schrodinger Equation on the Circle / 4.6.2：
Recurrence of Random Walk / 4.7：
Applications to Probability Theory / 5：
Basic Definitions / 5.1：
The Central Limit Theorem / 5.2.1：
Restatement in Terms of Independent Random Variables / 5.2.1.1：
Extension to Gap Series / 5.3：
Extension to Abel Sums / 5.3.1：
Weak Convergence of Measures / 5.4：
An Improved Continuity Theorem / 5.4.1：
Another Proof of Bochner's Theorem / 5.4.1.1：
Convolution Semigroups / 5.5：
The Berry-Esseen Theorem / 5.6：
Extension to Different Distributions / 5.6.1：
The Law of the Iterated Logarithm / 5.7：
Introduction to Wavelets / 6：
Heuristic Treatment of the Wavelet Transform / 6.1：
Wavelet Transform / 6.2：
Wavelet Characterization of Smoothness / 6.2.0.1：
Haar Wavelet Expansion / 6.3：
Haar Functions and Haar Series / 6.3.1：
Haar Sums and Dyadic Projections / 6.3.2：
Completeness of the Haar Functions / 6.3.3：
Haar Series in C[subscript 0] and L[subscript p] Spaces / 6.3.3.1：
Pointwise Convergence of Haar Series / 6.3.3.2：
Construction of Standard Brownian Motion / 6.3.4：
Haar Function Representation of Brownian Motion / 6.3.5：
Proof of Continuity / 6.3.6：
Levy's Modulus of Continuity / 6.3.7：
Multiresolution Analysis / 6.4：
Orthonormal Systems and Riesz Systems / 6.4.1：
Scaling Equations and Structure Constants / 6.4.2：
From Scaling Function to MRA / 6.4.3：
Additional Remarks / 6.4.3.1：
Meyer Wavelets / 6.4.4：
From Scaling Function to Orthonormal Wavelet / 6.4.5：
Direct Proof that V[subscript 1] [minus sign in circle] V[subscript 0] Is Spanned by {[Psi](t - k)}[subscript k[set membership]Z] / 6.4.5.1：
Null Integrability of Wavelets Without Scaling Functions / 6.4.5.2：
Wavelets with Compact Support / 6.5：
From Scaling Filter to Scaling Function / 6.5.1：
Explicit Construction of Compact Wavelets / 6.5.2：
Daubechies Recipe / 6.5.2.1：
Hernandez-Weiss Recipe / 6.5.2.2：
Smoothness of Wavelets / 6.5.3：
A Negative Result / 6.5.3.1：
Cohen's Extension of Theorem 6.5.1 / 6.5.4：
Convergence Properties of Wavelet Expansions / 6.6：
Wavelet Series in L[superscript p] Spaces / 6.6.1：
Large Scale Analysis / 6.6.1.1：
Almost-Everywhere Convergence / 6.6.1.2：
Convergence at a Preassigned Point / 6.6.1.3：
Jackson and Bernstein Approximation Theorems / 6.6.2：
Wavelets in Several Variables / 6.7：
Two Important Examples / 6.7.1：
Tensor Product of Wavelets / 6.7.1.1：
General Formulation of MRA and Wavelets in R[superscript d] / 6.7.2：
Notations for Subgroups and Cosets / 6.7.2.1：
Riesz Systems and Orthonormal Systems in R[superscript d] / 6.7.2.2：
Scaling Equation and Structure Constants / 6.7.2.3：
Existence of the Wavelet Set / 6.7.2.4：
Proof That the Wavelet Set Spans V[subscript 1] [minus sign in circle] V[subscript 0] / 6.7.2.5：
Cohen's Theorem in R[superscript d] / 6.7.2.6：
Examples of Wavelets in R[superscript d] / 6.7.3：
References
Notations
Index
Fourier Series on the Circle / 1：
Motivation and Heuristics / 1.1：
Motivation from Physics / 1.1.1：
32.

図書
図書
32. Fourier analysis : an introduction
Elias M. Stein & Rami Shakarchi
出版情報: Princeton, N.J. : Princeton University Press, c2003  xvi, 311 p. ; 24 cm
シリーズ名: Princeton lectures in analysis ; 1
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33.

図書
図書
33. Fourier analysis and partial differential equations
Rafael José Iorio, Jr., Valéria de Magalhães Iorio
出版情報: Cambridge : Cambridge University Press, 2001  xi, 411 p. ; 24 cm
シリーズ名: Cambridge studies in advanced mathematics ; 70
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Fourier Series and Periodic Distributions / Part I：
Preliminaries / 1：
Fourier series: basic theory / 2：
Periodic distributions and Sobolev spaces / 3：
Applications to Partial Differential Equations / Part II：
Linear equations / 4：
Nonlinear evolution equations / 5：
The Korteweg-de Vries / 6：
Distributions, Fourier transforms and linear equations / Part III：
KdV, BO and friends / 8：
Tools from the theory of ODEs / Appendix A：
Commutator estimates / Appendix B：
Bibliography
Index
Fourier Series and Periodic Distributions / Part I：
Preliminaries / 1：
Fourier series: basic theory / 2：
34.

図書
図書
34. Principles of fourier analysis
Kenneth B. Howell
出版情報: Boca Raton, FL : Chapman & Hall/CRC, c2001  776 p. ; 26 cm
シリーズ名: Studies in advanced mathematics
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Preface
Sample Courses
Preliminaries / I：
The Starting Point / 1：
Fourier's Bold Conjecture / 1.1：
Mathematical Preliminaries and the Following Chapters / 1.2：
Basic Terminology, Notation, and Conventions / 2：
Numbers / 2.1：
Functions, Formulas, and Variables / 2.2：
Operators and Transforms / 2.3：
Basic Analysis I: Continuity and Smoothness / 3：
(Dis)Continuity / 3.1：
Differentiation / 3.2：
Basic Manipulations and Smoothness / 3.3：
Addenda / 3.4：
Basic Analysis II: Integration and Infinite Series / 4：
Integration / 4.1：
Infinite Series (Summations) / 4.2：
Symmetry and Periodicity / 5：
Even and Odd Functions / 5.1：
Periodic Functions / 5.2：
Sines and Cosines / 5.3：
Elementary Complex Analysis / 6：
Complex Numbers / 6.1：
Complex-Valued Functions / 6.2：
The Complex Exponential / 6.3：
Functions of a Complex Variable / 6.4：
Functions of Several Variables / 7：
Basic Extensions / 7.1：
Single Integrals of Functions with Two Variables / 7.2：
Double Integrals / 7.3：
Addendum / 7.4：
Fourier Series / II：
Heuristic Derivation of the Fourier Series Formulas / 8：
The Frequencies / 8.1：
The Coefficients / 8.2：
Summary / 8.3：
The Trigonometric Fourier Series / 9：
Defining the Trigonometric Fourier Series / 9.1：
Computing the Fourier Coefficients / 9.2：
Partial Sums and Graphing / 9.3：
Fourier Series over Finite Intervals (Sine and Cosine Series) / 10：
The Basic Fourier Series / 10.1：
The Fourier Sine Series / 10.2：
The Fourier Cosine Series / 10.3：
Using These Series / 10.4：
Inner Products, Norms, and Orthogonality / 11：
Inner Products / 11.1：
The Norm of a Function / 11.2：
Orthogonal Sets of Functions / 11.3：
Orthogonal Function Expansions / 11.4：
The Schwarz Inequality for Inner Products / 11.5：
Bessel's Inequality / 11.6：
The Complex Exponential Fourier Series / 12：
Derivation / 12.1：
Notation and Terminology / 12.2：
Computing the Coefficients / 12.3：
Partial Sums / 12.4：
Convergence and Fourier's Conjecture / 13：
Pointwise Convergence / 13.1：
Uniform and Nonuniform Approximations / 13.2：
Convergence in Norm / 13.3：
The Sine and Cosine Series / 13.4：
Convergence and Fourier's Conjecture: The Proofs / 14：
Basic Theorem on Pointwise Convergence / 14.1：
Convergence for a Particular Saw Function / 14.2：
Convergence for Arbitrary Saw Functions / 14.3：
Derivatives and Integrals of Fourier Series / 15：
Differentiation of Fourier Series / 15.1：
Differentiability and Convergence / 15.2：
Integrating Periodic Functions and Fourier Series / 15.3：
Sine and Cosine Series / 15.4：
Applications / 16：
The Heat Flow Problem / 16.1：
The Vibrating String Problem / 16.2：
Functions Defined by Infinite Series / 16.3：
Verifying the Heat Flow Problem Solution / 16.4：
Classical Fourier Transforms / III：
Heuristic Derivation of the Classical Fourier Transform / 17：
Riemann Sums over the Entire Real Line / 17.1：
The Derivation / 17.2：
Integrals on Infinite Intervals / 17.3：
Absolutely Integrable Functions / 18.1：
The Set of Absolutely Integrable Functions / 18.2：
Many Useful Facts / 18.3：
Functions with Two Variables / 18.4：
The Fourier Integral Transforms / 19：
Definitions, Notation, and Terminology / 19.1：
Near-Equivalence / 19.2：
Linearity / 19.3：
Invertibility / 19.4：
Other Integral Formulas (A Warning) / 19.5：
Some Properties of the Transformed Functions / 19.6：
Classical Fourier Transforms and Classically Transformable Functions / 20：
The First Extension / 20.1：
The Set of Classically Transformable Functions / 20.2：
The Complete Classical Fourier Transforms / 20.3：
What Is and Is Not Classically Transformable? / 20.4：
Duration, Bandwidth, and Two Important Sets of Classically Transformable Functions / 20.5：
More on Terminology, Notation, and Conventions / 20.6：
Some Elementary Identities: Translation, Scaling, and Conjugation / 21：
Translation / 21.1：
Scaling / 21.2：
Practical Transform Computing / 21.3：
Complex Conjugation and Related Symmetries / 21.4：
Differentiation and Fourier Transforms / 22：
The Differentiation Identities / 22.1：
Rigorous Derivation of the Differential Identities / 22.2：
Higher Order Differential Identities / 22.3：
Anti-Differentiation and Integral Identities / 22.4：
Gaussians and Other Very Rapidly Decreasing Functions / 23：
Basic Gaussians / 23.1：
General Gaussians / 23.2：
Gaussian-Like Functions / 23.3：
Complex Translation and Very Rapidly Decreasing Functions / 23.4：
Convolution and Transforms of Products / 24：
Derivation of the Convolution Formula / 24.1：
Basic Formulas and Properties of Convolution / 24.2：
Algebraic Properties / 24.3：
Computing Convolutions / 24.4：
Existence, Smoothness, and Derivatives of Convolutions / 24.5：
Convolution and Fourier Analysis / 24.6：
Correlation, Square-Integrable Functions, and the Fundamental Identity of Fourier Analysis / 25：
Correlation / 25.1：
Square-Integrable/Finite Energy Functions / 25.2：
The Fundamental Identity / 25.3：
Identity Sequences / 26：
An Elementary Identity Sequence / 26.1：
General Identity Sequences / 26.2：
Gaussian Identity Sequences / 26.3：
Verifying Identity Sequences / 26.4：
An Application (with Exercises) / 26.5：
Generalizing the Classical Theory: A Naive Approach / 27：
Delta Functions / 27.1：
Transforms of Periodic Functions / 27.2：
Arrays of Delta Functions / 27.3：
The Generalized Derivative / 27.4：
Fourier Analysis in the Analysis of Systems / 28：
Linear, Shift-Invariant Systems / 28.1：
Computing Outputs for LSI Systems / 28.2：
Gaussians as Test Functions, and Proofs of Some Important Theorems / 29：
Testing for Equality with Gaussians / 29.1：
The Fundamental Theorem on Invertibility / 29.2：
The Fourier Differential Identities / 29.3：
The Fundamental and Convolution Identities of Fourier Analysis / 29.4：
Generalized Functions and Fourier Transforms / IV：
A Starting Point for the Generalized Theory / 30：
Starting Points / 30.1：
Gaussian Test Functions / 31：
The Space of Gaussian Test Functions / 31.1：
On Using the Space of Gaussian Test Functions / 31.2：
Two Other Test Function Spaces and a Confession / 31.3：
More on Gaussian Test Functions / 31.4：
Norms and Operational Continuity / 31.5：
Generalized Functions / 32：
Functionals / 32.1：
Basic Algebra of Generalized Functions / 32.2：
Generalized Functions Based on Other Test Function Spaces / 32.4：
Some Consequences of Functional Continuity / 32.5：
The Details of Functional Continuity / 32.6：
Sequences and Series of Generalized Functions / 33：
Sequences and Limits / 33.1：
A Little More on Delta Functions / 33.2：
Basic Transforms of Generalized Fourier Analysis / 33.4：
Fourier Transforms / 34.1：
Generalized Scaling of the Variable / 34.2：
Generalized Translation/Shifting / 34.3：
Transforms of Limits and Series / 34.4：
Adjoint-Defined Transforms in General / 34.6：
Generalized Complex Conjugation / 34.7：
Generalized Products, Convolutions, and Definite Integrals / 35：
Multiplication and Convolution / 35.1：
Definite Integrals of Generalized Functions / 35.2：
Appendix: On Defining Generalized Products and Convolutions / 35.3：
Periodic Functions and Regular Arrays / 36：
Periodic Generalized Functions / 36.1：
Fourier Series for Periodic Generalized Functions / 36.2：
On Proving Theorem 36.5 / 36.3：
General Solutions to Simple Equations and the Pole Functions / 37：
Basics on Solving Simple Algebraic Equations / 37.1：
Homogeneous Equations with Polynomial Factors / 37.2：
Nonhomogeneous Equations with Polynomial Factors / 37.3：
The Pole Functions / 37.4：
Pole Functions in Transforms, Products, and Solutions / 37.5：
The Discrete Theory / V：
Periodic, Regular Arrays / 38：
The Index Period and Other Basic Notions / 38.1：
Fourier Series and Transforms of Periodic, Regular Arrays / 38.2：
Sampling and the Discrete Fourier Transform / 39：
Some General Conventions and Terminology / 39.1：
Sampling and the Discrete Approximation / 39.2：
The Discrete Approximation and Its Transforms / 39.3：
The Discrete Fourier Transforms / 39.4：
Discrete Transform Identities / 39.5：
Fast Fourier Transforms / 39.6：
Appendices
Fourier Transforms of Some Common Functions / Table A.1：
Identities for the Fourier Transforms / Table A.2：
References
Answers to Selected Exercises
Index
Preface
Sample Courses
Preliminaries / I：
35.

図書
図書
35. A first course in wavelets with Fourier analysis
Albert Boggess, Francis J. Narcowich
出版情報: Upper Saddle River, NJ : Prentice Hall, c2001  xix, 283 p. ; 25 cm
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Preface
Acknowledgments
Inner Product Spaces / 0：
Motivation / 0.1：
Definition of Inner Product / 0.2：
The Spaces L[superscript 2] and l[superscript 2] / 0.3：
Definitions / 0.3.1：
Convergence in L[superscript 2] versus Uniform Convergence / 0.3.2：
Schwarz and Triangle Inequalities / 0.4：
Orthogonality / 0.5：
Definitions and Examples / 0.5.1：
Orthogonal Projections / 0.5.2：
Gram-Schmidt Orthogonalization / 0.5.3：
Linear Operators and Their Adjoints / 0.6：
Linear Operators / 0.6.1：
Adjoints / 0.6.2：
Least Squares and Linear Predictive Coding / 0.7：
Best Fit Line for Data / 0.7.1：
General Least Squares Algorithm / 0.7.2：
Linear Predictive Coding / 0.7.3：
Exercises / 0.8：
Fourier Series / 1：
Introduction / 1.1：
Historical Perspective / 1.1.1：
Signal Analysis / 1.1.2：
Partial Differential Equations / 1.1.3：
Computation of Fourier Series / 1.2：
On the Interval -[pi] [less than or equal] x [less than or equal] [pi] / 1.2.1：
Other Intervals / 1.2.2：
Cosine and Sine Expansions / 1.2.3：
Examples / 1.2.4：
The Complex Form of Fourier Series / 1.2.5：
Convergence Theorems for Fourier Series / 1.3：
The Riemann-Lebesgue Lemma / 1.3.1：
Convergence at a Point of Continuity / 1.3.2：
Convergence at a Point of Discontinuity / 1.3.3：
Uniform Convergence / 1.3.4：
Convergence in the Mean / 1.3.5：
The Fourier Transform / 1.4：
Informal Development of the Fourier Transform / 2.1：
The Fourier Inversion Theorem / 2.1.1：
Properties of the Fourier Transform / 2.1.2：
Basic Properties / 2.2.1：
Fourier Transform of a Convolution / 2.2.2：
Adjoint of the Fourier Transform / 2.2.3：
Plancherel Formula / 2.2.4：
Linear Filters / 2.3：
Time Invariant Filters / 2.3.1：
Causality and the Design of Filters / 2.3.2：
The Sampling Theorem / 2.4：
The Uncertainty Principle / 2.5：
Discrete Fourier Analysis / 2.6：
The Discrete Fourier Transform / 3.1：
Definition of Discrete Fourier Transform / 3.1.1：
Properties of the Discrete Fourier Transform / 3.1.2：
The Fast Fourier Transform / 3.1.3：
The FFT Approximation to the Fourier Transform / 3.1.4：
Application--Parameter Identification / 3.1.5：
Application--Discretizations of Ordinary Differential Equations / 3.1.6：
Discrete Signals / 3.2：
Time Invariant, Discrete Linear Filters / 3.2.1：
Z-Transform and Transfer Functions / 3.2.2：
Haar Wavelet Analysis / 3.3：
Why Wavelets? / 4.1：
Haar Wavelets / 4.2：
The Haar Scaling Function / 4.2.1：
Basic Properties of the Haar Scaling Function / 4.2.2：
The Haar Wavelet / 4.2.3：
Haar Decomposition and Reconstruction Algorithms / 4.3：
Decomposition / 4.3.1：
Reconstruction / 4.3.2：
Filters and Diagrams / 4.3.3：
Summary / 4.4：
Multiresolution Analysis / 4.5：
The Multiresolution Framework / 5.1：
Definition / 5.1.1：
The Scaling Relation / 5.1.2：
The Associated Wavelet and Wavelet Spaces / 5.1.3：
Decomposition and Reconstruction Formulas: A Tale of Two Bases / 5.1.4：
Implementing Decomposition and Reconstruction / 5.1.5：
The Decomposition Algorithm / 5.2.1：
The Reconstruction Algorithm / 5.2.2：
Processing a Signal / 5.2.3：
Fourier Transform Criteria / 5.3：
The Scaling Function / 5.3.1：
Orthogonality via the Fourier Transform / 5.3.2：
The Scaling Equation via the Fourier Transform / 5.3.3：
Iterative Procedure for Constructing the Scaling Function / 5.3.4：
The Daubechies Wavelets / 5.4：
Daubechies's Construction / 6.1：
Classification, Moments, and Smoothness / 6.2：
Computational Issues / 6.3：
The Scaling Function at Dyadic Points / 6.4：
Other Wavelet Topics / 6.5：
Computational Complexity / 7.1：
Wavelet Algorithm / 7.1.1：
Wavelet Packets / 7.1.2：
Wavelets in Higher Dimensions / 7.2：
Relating Decomposition and Reconstruction / 7.3：
Transfer Function Interpretation / 7.3.1：
Wavelet Transform / 7.4：
Definition of the Wavelet Transform / 7.4.1：
Inversion Formula for the Wavelet Transform / 7.4.2：
Technical Matters / Appendix A：
Proof of the Fourier Inversion Formula / A.1：
Rigorous Proof of Theorem 5.17 / A.2：
Proof of Theorem 5.10 / A.2.1：
Proof of the Convergence Part of Theorem 5.23 / A.2.2：
Matlab Routines / Appendix B：
General Compression Routine / B.1：
Use of MATLAB's FFT Routine for Filtering and Compression / B.2：
Sample Routines Using MATLAB's Wavelet Toolbox / B.3：
MATLAB Code for the Algorithms in Section 5.2 / B.4：
Bibliography
Index
Preface
Acknowledgments
Inner Product Spaces / 0：
36.

図書
図書
36. Fourier analysis
Javier Duoandikoetxea ; translated and revised by David Cruz-Uribe
出版情報: Providence, R.I. : American Mathematical Society, c2001  xviii, 222 p. ; 26 cm
シリーズ名: Graduate studies in mathematics ; v. 29
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Fourier series and integrals
The Hardy-Littlewood maximal function
The Hilbert transform Singular integrals (I)
Singular integrals (II)
$H^1$ and $BMO$ Weighted inequalities
Littlewood-Paley theory and multipliers
The $T1$ theorem
Bibliography
Index
Fourier series and integrals
The Hardy-Littlewood maximal function
The Hilbert transform Singular integrals (I)
37.

図書
図書
37. Ordinary and partial differential equations : with special functions, Fourier series, and boundary value problems (: pbk)
Ravi P. Agarwal, Donal O'Regan
出版情報: New York ; London : Springer, c2009  xiv, 410 p. ; 24 cm
シリーズ名: Universitext
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Preface
Solvable Differential Equations / 1：
Second-Order Differential Equations / 2：
Preliminaries to Series Solutions / 3：
Solution at an Ordinary Point / 4：
Solution at a Singular Point / 5：
Solution at a Singular Point (Cont'd.) / 6：
Legendre Polynomials and Functions / 7：
Chebyshev, Hermite and Laguerre Polynomials / 8：
Bessel Functions / 9：
Hypergeometric Functions / 10：
Piecewise Continuous and Periodic Functions / 11：
Orthogonal Functions and Polynomials / 12：
Orthogonal Functions and Polynomials (Cont'd.) / 13：
Boundary Value Problems / 14：
Boundary Value Problems (Cont'd.) / 15：
Green's Functions / 16：
Regular Perturbations / 17：
Singular Perturbations / 18：
Sturm-Liouville Problems / 19：
Eigenfunction Expansions / 20：
Eigenfunction Expansions (Cont'd.) / 21：
Convergence of the Fourier Series / 22：
Convergence of the Fourier Series (Cont'd.) / 23：
Fourier Series Solutions of Ordinary Differential Equations / 24：
Partial Differential Equations / 25：
First-Order Partial Differential Equations / 26：
Solvable Partial Differential Equations / 27：
The Canonical Forms / 28：
The Method of Separation of Variables / 29：
The One-Dimensional Heat Equation / 30：
The One-Dimensional Heat Equation (Cont'd.) / 31：
The One-Dimensional Wave Equation / 32：
The One-Dimensional Wave Equation (Cont'd.) / 33：
Laplace Equation in Two Dimensions / 34：
Laplace Equation in Polar Coordinates / 35：
Two-Dimensional Heat Equation / 36：
Two-Dimensional Wave Equation / 37：
Laplace Equation in Three Dimensions / 38：
Laplace Equation in Three Dimensions (Cont'd.) / 39：
Nonhomogeneous Equations / 40：
Fourier Integral and Transforms / 41：
Fourier Integral and Transforms (Cont'd.) / 42：
Fourier Transform Method for Partial DEs / 43：
Fourier Transform Method for Partial DEs (Cont'd.) / 44：
Laplace Transforms / 45：
Laplace Transforms (Cont'd.) / 46：
Laplace Transform Method for Ordinary DEs / 47：
Laplace Transform Method for Partial DEs / 48：
Well-Posed Problems / 49：
Verification of Solutions / 50：
References for Further Reading
Index
Preface
Solvable Differential Equations / 1：
Second-Order Differential Equations / 2：
38.

図書
図書
38. Fourier analysis
Eric Stade
出版情報: Hoboken, N.J. : John Wiley & Sons, c2005  xxiv, 488 p. ; 25 cm
シリーズ名: Pure and applied mathematics
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Preface
Introduction
Fourier Coefficients and Fourier Series / 1：
Fourier Series and Boundary Value Problems / 2：
L2 Spaces: Optimal Contexts for Fourier Series / 3：
Sturm-Liouville Problems / 4：
A Splat and a Spike / 5：
Fourier Transforms and Fourier Integrals / 6：
Special Topics and Applications / 7：
Local Frequency Analysis and Wavelets / 8：
Appendix
References
Index
Preface
Introduction
Fourier Coefficients and Fourier Series / 1：
39.

図書
図書
39. Fourier analysis
Larry Baggett and Watson Fulks
出版情報: Boulder, CO : Anjou Press, c1979  viii, 183 p. ; 25 cm
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40.

図書
図書
40. A guide to distribution theory and Fourier transforms (: hard ; : pbk)
Robert S. Strichartz
出版情報: New Jersey : World Scientific, c2003  x, 226 p. ; 24 cm
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Preface
What are Distributions? / 1：
Generalized functions and test functions / 1.1：
Examples of distributions / 1.2：
What good are distributions? / 1.3：
Problems / 1.4：
The Calculus of Distributions / 2：
Functions as distributions / 2.1：
Operations on distributions / 2.2：
Adjoint identities / 2.3：
Consistency of derivatives / 2.4：
Distributional solutions of differential equations / 2.5：
Fourier Transforms / 2.6：
From Fourier series to Fourier integrals / 3.1：
The Schwartz class S / 3.2：
Properties of the Fourier transform on S / 3.3：
The Fourier inversion formula on S / 3.4：
The Fourier transform of a Gaussian / 3.5：
Fourier Transforms of Tempered Distributions / 3.6：
The definitions / 4.1：
Examples / 4.2：
Convolutions with tempered distributions / 4.3：
Solving Partial Differential Equations / 4.4：
The Laplace equation / 5.1：
The heat equation / 5.2：
The wave equation / 5.3：
Schrodinger's equation and quantum mechanics / 5.4：
The Structure of Distributions / 5.5：
The support of a distribution / 6.1：
Structure theorems / 6.2：
Distributions with point support / 6.3：
Positive distributions / 6.4：
Continuity of distribution / 6.5：
Approximation by test functions / 6.6：
Local theory of distributions / 6.7：
Distributions on spheres / 6.8：
Fourier Analysis / 6.9：
The Riemann-Lebesgue lemma / 7.1：
Paley-Wiener theorems / 7.2：
The Poisson summation formula / 7.3：
Probability measures and positive definite functions / 7.4：
The Heisenberg uncertainty principle / 7.5：
Hermite functions / 7.6：
Radial Fourier transforms and Bessel functions / 7.7：
Haar functions and wavelets / 7.8：
Sobolev Theory and Microlocal Analysis / 7.9：
Sobolev inequalities / 8.1：
Sobolev spaces / 8.2：
Elliptic partial differential equations (constant coefficients) / 8.3：
Pseudodifferential operators / 8.4：
Hyperbolic operators / 8.5：
The wave front set / 8.6：
Microlocal analysis of singularities / 8.7：
Suggestions for Further Reading / 8.8：
Index
Preface
What are Distributions? / 1：
Generalized functions and test functions / 1.1：
41.

図書
図書
41. Fourier analysis and nonlinear partial differential equations (: hbk ; : pbk)
Hajer Bahouri, Jean-Yves Chemin, Raphaël Danchin
出版情報: Heidelberg : Springer, c2011  xv, 523 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 343
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Basic Analysis / 1：
Basic Real Anslysis / 1.1：
Holder and Convolution Inequslities / 1.1.1：
The Atomic Decomposition / 1.1.2：
Proof of Refined Young Inequslityp8 / 1.1.3：
A Bilinear Interpolation Theorem / 1.1.4：
A Linear Interpolation Result / 1.1.5：
The Hardy-Littlewood Maximal Function / 1.1.6：
The Fourier Transform / 1.2：
Fourier Transforms of Functions and the Schwartz Space / 1.2.1：
Tempered Distributions and the Fourier Transform / 1.2.2：
A Few Calculations of Fourier Transforms / 1.2.3：
Homogeneous Sobolev Spaces / 1.3：
Definition and Basic Properties / 1.3.1：
Sobolev Embedding in Lebesgue Spaces / 1.3.2：
The Limit Case Hd/2 / 1.3.3：
The Embedding Theorem in Hölder Spaces / 1.3.4：
Nonhomogeneous Sobolev Spaces on Rd / 1.4：
Embedding / 1.4.1：
A Density Theorem / 1.4.3：
Hardy Inequality / 1.4.4：
References and Remarks / 1.5：
Littlewood-Paley Theory / 2：
Functions with Compactly Supported Fourier Transforms / 2.1：
Bernstein-Type Lemmas / 2.1.1：
The Smoothing Effect of Heat Flow / 2.1.2：
The Action of a Diffeomorphism / 2.1.3：
The Effects of Some Nonlinear Functions / 2.1.4：
Dyadic Partition of Unity / 2.2：
Homogeneous Besov Spaces / 2.3：
Characterizations of Homogeneous Besov Spaces / 2.4：
Besov Spaces, Lebesgue Spaces, and Refined Inequalities / 2.5：
Homogeneous Paradifferential Calculus / 2.6：
Homogeneous Bony Decomposition / 2.6.1：
Action of Smooth Functions / 2.6.2：
Time-Space Besov Spaces / 2.6.3：
Nonhomogeneous Besov Spaces / 2.7：
Nonhomogeneous Paradifferential Calculus / 2.8：
The Bony Decomposition / 2.8.1：
The Paralinearization Theorem / 2.8.2：
Besov Spaces and Compact Embeddings / 2.9：
Commutator Estimates / 2.10：
Around the Space B&infty;,&infty;1 / 2.11：
Transport and Transport-Diffusion Equations / 2.12：
Ordinary Differential Equations / 3.1：
The Cauchy-Lipschitz Theorem Revisited / 3.1.1：
Estimates for the Flow / 3.1.2：
A Blow-up Criterion for Ordinary Differential Equations / 3.1.3：
Transport Equations: The Lipschitz Case / 3.2：
A Priori Estimates in General Besov Spaces / 3.2.1：
Refined Estimates in Besov Spaces with Index 0 / 3.2.2：
Solving the Transport Equation in Besov Spaces / 3.2.3：
Application to a Shallow Water Equation / 3.2.4：
Losing Estimates for Transport Equations / 3.3：
Linear Loss of Regularity in Besov Spaces / 3.3.1：
The Exponential Loss / 3.3.2：
Limited Loss of Regularity / 3.3.3：
A Few Applications / 3.3.4：
Transport-Diffusion Equations / 3.4：
A Priori Estimates / 3.4.1：
Exponential Decay / 3.4.2：
Quasilinear Symmetric Systems / 3.5：
Definition and Examples / 4.1：
Linear Symmetric Systems / 4.2：
The Well-posedness of Linear Symmetric Systems / 4.2.1：
Finite Propagation Speed / 4.2.2：
Further Well-posedness Results for Linear Symmetric Systems / 4.2.3：
The Resolution of Quasilinear Symmetric Systems / 4.3：
Paralinearization and Energy Estimates / 4.3.1：
Convergence of the Scheme / 4.3.2：
Completion of the Proof of Existence / 4.3.3：
Uniqueness and Continuation Criterion / 4.3.4：
Data with Critical Regularity and Blow-up Criteria / 4.4：
Critical Besov Regularity / 4.4.1：
A Refined Blow-up Crndition / 4.4.2：
Continuity of the Flow Map / 4.5：
The Incompressible Navier-Stokes System / 4.6：
Basic Facts Concerning the Navier-Stokes System / 5.1：
Well-posedness in Sobolev Spaces / 5.2：
A General Result / 5.2.1：
The Behavior of the Hd/2-1 Norm Near 0 / 5.2.2：
Results Related to the Structure of the System / 5.3：
The Particular Case of Dimension Two / 5.3.1：
The Case of Dimension Three / 5.3.2：
An Elementary Lp Approach / 5.4：
The Endpoint Space for Picard's Scheme / 5.5：
The Use of the L1-smoothing Effect of the Heat Flow / 5.6：
The Cannone-Meyer-Planchon Theorem Revisited / 5.6.1：
The Flow of the Solutions of the Navier-Stokes System / 5.6.2：
Anisotropic Viscosity / 5.7：
The Case of L2 Data with One Vertical Derivative in L2 / 6.1：
A Global Existence Result in Anisotropic Besov Spaces / 6.2：
Anisotropic Localization in Fourier Space / 6.2.1：
The Functional Framework / 6.2.2：
Statement of the Main Result / 6.2.3：
Some Technical Lemmas / 6.2.4：
The Proof of Existence / 6.3：
The Proof of Uniqueness / 6.4：
Euler System for Perfect Incompressible Fluids / 6.5：
Local Well-posedness Results for Inviscid Fluids / 7.1：
The Biot-Savart Law / 7.1.1：
Estimates for the Pressure / 7.1.2：
Another Formulation of the Euler System / 7.1.3：
Local Existence of Smooth Solutions / 7.1.4：
Uniqueness / 7.1.5：
Continuation Criteria / 7.1.6：
Global Existence Results in Dimension Two / 7.2：
Smooth Solutions / 7.2.1：
The Borderline Case / 7.2.2：
The Yudovich Theorem / 7.2.3：
The Inviscid Limit / 7.3：
Regularity Results for the Navier-Stokes System / 7.3.1：
The Smooth Case / 7.3.2：
The Rough Case / 7.3.3：
Viscous Vortex Patches / 7.4：
Results Related to Striated Regularity / 7.4.1：
A Stationary Estimate for the Velocity Field / 7.4.2：
Uniform Estimates for Striated Regularity / 7.4.3：
A Global Convergence Result for Striated Regularity / 7.4.4：
Application to Smooth Vortex Patches / 7.4.5：
Strichartz Estimates and Applications to Semilinear Dispersive Equations / 7.5：
Examples of Dispersive Estimates / 8.1：
The Dispersive Estimate for the Free Transport Equation / 8.1.1：
The Dispersive Estimates for the Schrdillger Equation / 8.1.2：
Integral of Oscillating Functions / 8.1.3：
Dispersive Estimates for the Wave Equation / 8.1.4：
The L2 Boundedness of Some Fourier Integral Operators / 8.1.5：
Billnear Methods / 8.2：
The Duality Method and the TT* Argument / 8.2.1：
Strichartz Estimates: The Case q > 2 / 8.2.2：
Strichartz Estimates: The Endpoint Case q = 2 / 8.2.3：
Application to the Cubic Semilinear Schrödinger Equation / 8.2.4：
Strichartz Estimates for the Wave Equation / 8.3：
The Basic Strichartz Estimate / 8.3.1：
The Refined Strichartz Estimate / 8.3.2：
The Qulntic Wave Equation in R3 / 8.4：
The Cubic Wave Equation in R3 / 8.5：
Solutions in H1 / 8.5.1：
Local and Global Well-posedness for Rough Data / 8.5.2：
The Nonlinear Interpolation Method / 8.5.3：
Application to a Class of Semilinear Wave Equations / 8.6：
Smoothing Effect in Quasilinear Wave Equations / 8.7：
A Well-posedness Result Based on an Energy Method / 9.1：
The Main Statement and the Strategy of its Proof / 9.2：
Refined Paralinearization of the Wave Equation / 9.3：
Reduction to a Microlocal Strichartz Estimate / 9.4：
Microlocal Strichartz Estimates / 9.5：
A Rather General Statement / 9.5.1：
Geometrical Optics / 9.5.2：
The Solution of the Eikonal Equation / 9.5.3：
The Transport Equation / 9.5.4：
The Approximation Theorem / 9.5.5：
The Proof of Theorem 9.16 / 9.5.6：
The Compressible Navier-Stokes System / 9.6：
About the Model / 10.1：
General Overview / 10.1.1：
The Barotropic Navier-Stokes Equations / 10.1.2：
Local Theory for Data with Critical Regularity / 10.2：
Scaling Invariance and Statement of the Main Result / 10.2.1：
Existence of a Local Solution / 10.2.2：
A Continuation Criterion / 10.2.4：
Local Theory for Data Bounded Away from the Vacuum / 10.3：
A Priori Estimates for the Linearized Momentum Equation / 10.3.1：
Global Existence for Small Data / 10.3.2：
Statement of the Results / 10.4.1：
A Spectral Analysis of the Linearized Equation / 10.4.2：
A Prioli Estimates for the Linearized Equation / 10.4.3：
Proof of Global Existence / 10.4.4：
The Incompressible Limit / 10.5：
Main Results / 10.5.1：
The Case of Small Data with Critical Regularity / 10.5.2：
The Case of Large Data with More Regularity / 10.5.3：
References / 10.6：
List of Notations
Index
Basic Analysis / 1：
Basic Real Anslysis / 1.1：
Holder and Convolution Inequslities / 1.1.1：
42.

電子ブック
ＥＢ
42. Partial differential equations : topics in Fourier analysis. 2nd ed (: electronic bk)
M.W. Wong
出版情報: Taylor & Francis eBooks  1 online resource (ix, 197 p.)
シリーズ名: A Chapman & Hall book
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43.

電子ブック
ＥＢ
43. Fourier restriction, decoupling, and applications (: electronic bk)
Ciprian Demeter
出版情報:   1 online resource (xvi, 331 p.)
シリーズ名: Cambridge studies in advanced mathematics ; 184
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44.

電子ブック
ＥＢ
44. Fourier analysis on finite groups and applications (: electronic bk)
Audrey Terra
出版情報:   1 online resource (x, 442 p.)
シリーズ名: London Mathematical Society student texts ; 43
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Introduction
Cast of characters
Congruences and the quotient ring of the integers mod n / Part I：
The discrete Fourier transform on the finite circle / 1.2：
Graphs of Z/nZ, adjacency operators, eigenvalues / 1.3：
Four questions about Cayley graphs / 1.4：
Finite Euclidean graphs and three questions about their spectra / 1.5：
Random walks on Cayley graphs / 1.6：
Applications in geometry and analysis / 1.7：
The quadratic reciprocity law / 1.8：
The fast Fourier transform / 1.9：
The DFT on finite Abelian groups - finite tori / 1.10：
Error-correcting codes / 1.11：
The Poisson sum formula on a finite Abelian group / 1.12：
Some applications in chemistry and physics / 1.13：
The uncertainty principle / 1.14：
Fourier transform and representations of finite groups / Part II：
Induced representations / 2.2：
The finite ax + b group / 2.3：
Heisenberg group / 2.4：
Finite symmetric spaces - finite upper half planes Hq / 2.5：
Special functions on Hq - K-Bessel and spherical / 2.6：
The general linear group GL(2, Fq) / 2.7：
Selberg's trace formula and isospectral non-isomorphic graphs / 2.8：
The trace formula on finite upper half planes / 2.9：
The trace formula for a tree and Ihara's zeta function / 2.10：
Introduction
Cast of characters
Congruences and the quotient ring of the integers mod n / Part I：
45.

電子ブック
ＥＢ
45. Fourier analysis / ((ebook))
T. W. Körner ; with a foreword by Terence Tao
出版情報:   1 online resource (xiv, 591 pages)
シリーズ名: Cambridge mathematical library ;
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46.

図書
図書
46. Fourier analysis on number fields (: softcover)
Dinakar Ramakrishnan, Robert J. Valenza
出版情報: New York : Springer, c1999  xxi, 350 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 186
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