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1.

図書
図書
1. A course on Borel sets
S.M. Srivastava
出版情報: New York : Springer, c1998  xvi, 261 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 180
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2.

図書
図書
2. Handbook of Feynman path integrals
C. Grosche, F. Steiner
出版情報: Berlin : Springer, c1998  x, 449 p. ; 25 cm
シリーズ名: Springer tracts in modern physics : Ergebnisse der exakten Naturwissenschaften / editor, G. Höhler ; 145
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3.

図書
図書
3. Orthonormal systems and Banach space geometry (: pbk)
Albrecht Pietsch & Jörg Wenzel
出版情報: Cambridge : Cambridge University Press, 1998  ix, 553 p. ; 24 cm
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 70
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目次情報: 続きを見る
Preface
Introduction
Preliminaries
Ideal norms and operator ideals / 1：
Ideal norms associated with matrices / 2：
Ideal norms associated with orthonormal systems / 3：
Rademacher and Gauss ideal norms / 4：
Trigonometric ideal norms / 5：
Walsh ideal norms / 6：
Haar ideal norms / 7：
Unconditionality / 8：
Miscellaneous / 9：
Summaries
List of symbols
Bibliography
Index
Preface
Introduction
Preliminaries
4.

図書
図書
4. Oscillation theory of two-term differential equations
by Uri Elias
出版情報: Dordrecht : Kluwer, c1997  vii, 217 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 396
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Preface
Introduction / 0：
The Basic Lemma / 1：
Boundary Value Functions / 2：
Bases of Solutions / 3：
Comparison of Boundary Value Problems / 4：
Comparison Theorems for Two Equations / 5：
Disfocality and Its Characterization / 6：
Various Types of Disfocality / 7：
Solutions on an Infinite Interval / 8：
Disconjugacy and its Characterization / 9：
Eigenvalue Problems / 10：
More Extremal Points / 11：
Minors of the Wronskian / 12：
The Dominance Property of Solutions / 13：
References
Index
Preface
Introduction / 0：
The Basic Lemma / 1：
5.

図書
図書
5. Algebraic and differential topology of robust stability
Edmond A. Jonckheere ; with 79 pictures, computer generated by Chih-Yung Cheng, Chung-Kuang Chu, and Murilo G. Coutinho
出版情報: New York : Oxford University Press, 1997  xlvi, 576 p. ; 25 cm
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6.

図書
図書
6. Nonlinear partial differential equations in geometry and physics : the 1995 Barrett Lectures (: sz ; : us)
Garth Baker, Alexandre Freire, editors
出版情報: Basel : Birkhäuser, c1997  xi, 153 p. ; 24 cm
シリーズ名: Progress in nonlinear differential equations and their applications / editor, Haim Brezis ; v. 29
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7.

図書
図書
7. Partial differential equation methods in control and shape analysis
edited by Giuseppe Da Prato, Jean-Paul Zolésio
出版情報: New York : Marcel Dekker, c1997  viii, 331 p. ; 26 cm
シリーズ名: Lecture notes in pure and applied mathematics ; v. 188
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8.

図書
図書
8. Wavelets : an analysis tool (: hbk ; : pbk)
M. Holschneider
出版情報: Oxford : Clarendon Press , New York : Oxford University Press, 1995  xiii, 423 p. ; 24 cm
シリーズ名: Oxford mathematical monographs
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目次情報: 続きを見る
Introduction to wavelet analysis over R / Chapter 1：
A short motivation / 1：
Time-frequency analysis / 1.1：
Wavelets and approximation theory / 1.2：
Some easy properties of the wavelet transform / 2：
Wavelet transform in Fourier space / 3：
Co-variance of wavelet transforms / 4：
Voices, zooms, and convolutions / 5：
Laplace convolution / 5.1：
Scale convolution / 5.2：
Mellin transforms / 5.3：
The basic functions: the wavelets / 6：
The real wavelets / 7：
The progressive wavelets / 8：
Progressive wavelets with real-valued frequency representation / 8.1：
Chirp wavelets / 8.2：
On the modulus of progressive functions / 8.3：
Some explicit analysed functions and easy examples / 9：
The wavelet transform of pure frequencies / 9.1：
The real oscillations / 9.2：
The onsets / 9.4：
The wavelet analysis of a hyperbolic chirp / 9.5：
Interactions / 9.6：
Two deltas / 9.7：
Delta and pure frequency / 9.8：
The influence cone and easy localization properties / 10：
Polynomial localization / 11：
More precise results / 11.1：
The influence regions for pure frequencies / 12：
The space of highly time-frequency localized functions / 13：
The inversion formula / 14：
Fourier transform in wavelet space / 14.1：
Reconstruction with singular reconstruction wavelets / 15：
The wavelet synthesis operator / 16：
Reconstruction without reconstruction wavelet / 17：
Localization properties of the wavelet synthesis / 18：
Frequency localization / 18.1：
Time localization / 18.2：
Wavelet analysis over S[subscript +](R) / 19：
Schwartz space / 19.1：
The regularity of the image space / 19.2：
The reproducing kernel / 20：
The cross-kernel / 20.1：
The wavelet transform of a white noise / 21：
The wavelet transform in L[superscript 2](R) / 22：
The inverse wavelet transform / 23：
The wavelet transform over S[prime subscript +](R) / 24：
Definition of the wavelet transform / 24.1：
The wavelet transform on S[prime](R) / 25：
A class of operators / 26：
The derivation operator and Riesz potentials / 26.1：
Differentiation and integration over S[prime subscript 0](R) / 26.2：
Singular support of distributions / 27：
Bounded sets in S[subscript 0](R) and S[prime subscript 0](R) / 28：
Some explicit wavelet transforms of distributions / 29：
The distributions..., [Characters not reproducible] / 29.1：
The distributions [Characters not reproducible] / 29.2：
Extension to higher dimensions / 30：
Proof of Theorem 11.1.1 / 31：
Discretizing and periodizing the half-plane / Chapter 2：
Interpolation
Reconstruction over voices
One single voice / 2.1：
Infinitely many voices / 2.2：
An iteration procedure
Calderon-Zygmund operators: a first contact
Reconstruction over strips
The pointwise and uniform convergence of the inversion formula
Uniform convergence in L[superscript p](R), 1< p< [infinity] / 6.1：
Pointwise convergence in L[superscript p](R), 1 [greater than or equal] p< [infinity] / 6.2：
Pointwise convergence in L[superscript infinity](R) / 6.3：
The 'Gibbs' phenomenon for s[subscript epsilon, rho]
Gibbs phenomenon / 7.1：
No Gibbs phenomenon / 7.2：
Reconstruction over cones
The Poisson summation formula
Periodic functions
The periodizing operator
Sequences and sampling
The Fourier transform over the circle
Some sampling theorems
The continuous wavelet transform over T
Wavelet analysis of S(T) and S[prime](T) / 10.1：
The wavelet transform of L[superscript 2](T) / 10.2：
Sampling of voices
Frames and moments
Some wavelet frames
Irregular sampling / 13.1：
Calderon-Zygmund operators again / 13.2：
A functional calculus
The case of self-adjoint operators
The function e[superscript itA] / 14.2：
Multi-resolution analysis / Chapter 3：
Riesz bases
The Fourier space picture
Translation invariant orthonormal basis / 1.3：
Skew projections / 1.4：
Perfect sampling spaces / 1.5：
Splines / 1.6：
Exponential localization / 1.7：
Perfect sampling spaces of spline functions / 1.8：
Sampling spaces over Z, T, and Z/NZ
Sampling space over Z
Oversampling of sampling spaces / 2.3：
Sampling spaces over T / 2.4：
Periodizing a sampling space over R / 2.5：
Periodizing a sampling space over T / 2.6：
Sampling spaces over Z/NZ / 2.7：
Quadrature mirror filters in L[superscript 2](Z)
Completing a QMF-system / 3.1：
Complements over R / 3.2：
QMF over Z/NZ and complements over T / 3.3：
Multi-resolution analysis over R
Localization and regularity of [psi] / 4.1：
Examples of multi-resolution analysis and wavelets
The Haar system
Splines wavelets
Band-limited functions
Littlewood-Paley analysis / 5.4：
The partial reconstruction operator
Multi-resolution analysis of L[superscript 2](Z)
Isometrics and the shift operator
QMF and multi-resolution analysis over Z
Wavelets over Z / 7.3：
QMF and multi-resolution analysis
Compact support
An easy regularity estimate
The dyadic interpolation spaces
The Lagrange interpolation spaces
Compactly supported wavelets
Wavelet frames
Bi-orthogonal expansions
Bi-orthogonal expansions of L[superscript 2](Z) / 12.1：
Bi-orthogonal expansions in L[superscript 2](R) / 12.2：
QMF and loop groups
The group of unitary operators with [U, T[subscript 2]] = 0
Some subclasses of QMF / 13.3：
The factorization problem / 13.5：
Multi-resolution analysis over T
Multi-resolution analysis over Z/2[superscript M]Z
Computing the discrete wavelet transform
Filterbanks over Z / 16.1：
Computing the orthonormal wavelet transform over a dyadic grid / 16.2：
More general wavelet / 16.3：
Denser grids / 16.4：
Interpolation of the voices / 16.5：
The 'a trous' algorithm / 16.6：
Computation over Z/2[superscript N]Z / 16.7：
Computing over R by using data over Z/NZ
Fractal analysis and wavelet transforms / Chapter 4：
Self-similarity and the re-normalization group
Re-normalization in wavelet-space
The order of magnitude of wavelet coefficients
Inverse theorems for global regularity
The class of Zygmund
Inverse theorems for local regularity
Pointwise differentiability and wavelet analysis
The class W[superscript alpha]
Asymptotic behaviour at small scales
The Brownian motion
The Weierstrass non-differentiable function
The Riemann-Weierstrass function
The orbit of 0
The orbit of 1
The non-degenerated fixed points
The irrational points / 6.4：
The baker's map
A family of dynamical systems and fractal measures
Self-similar fractal measure
The evolution in wavelet space
Some fractal measures
Fractal dimensions
Capacity
The generalized fractal dimensions
Fractal dimensions and wavelet transforms
Time evolution and the dimension [kappa](2)
Local self-similarity and singularities
The f([alpha]) spectrum
On the fractality of orthonormal wavelets
Group theory as unifying language / Chapter 5：
Some notions of group theory
Direct sum of groups
Quotient groups
Homomorphisms
Representations
Schur's lemma
Group action
Invariant measures
Regular representations
Group convolutions / 1.9：
Square integrable representations / 1.10：
The 'wavelet' analysis associated to square integrable representations
A priori estimates
Transformation properties
Energy conservation
The left- and right-synthesis
Co-variance
The inversion formulae
On the constant c[subscript g,h]
More general reconstruction
The reproducing kernel equation
Fourier transform over Abelian groups
The Fourier transform
Group-translations
The convolution theorem
Periodizing, sampling, and M. Poisson
Sampling
Periodization
Sampling spaces over Abelian groups
The discrete wavelet transform over Abelian groups
A group of operators
Polynomial loops: the factorization problem / 10.3：
The wavelet transform in two dimensions
Reconstruction formulae / 11.2：
A class of inverse problems / 11.3：
The Radon transform as wavelet transform
The Radon-inversion formula
Functional analysis and wavelets / Chapter 6：
Some function spaces
Wavelet multipliers
The class of highly regular Calderon-Zygmund operators (CZOs)
The dilation co-variance
Fourier multipliers as highly regular CZO
Singular integrals as highly regular CZO
Pointwise properties of highly regular CZO
Littlewood-Paley theory
The Sobolev spaces
Bibliography
Index
Introduction to wavelet analysis over R / Chapter 1：
A short motivation / 1：
Time-frequency analysis / 1.1：
9.

図書
図書
9. Mathematical topics in fluid mechanics (v. 1 ; v. 2)
Pierre-Louis Lions
出版情報: Oxford : Clarendon Press, 1996-1998  2 v. ; 24 cm
シリーズ名: Oxford lecture series in mathematics and its applications ; 3, 10
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Compressible models / Part 2：
Compactness results for compressible isentropic Navier-Stokes equations / 5：
Stationary problems / 6：
Existence results for Cauchy problems / 7：
Related problems / 8：
A few facts about some function spaces / Appendix A：
On a weakly continuous product / Appendix B：
A remark on the limiting case for Sobolev inequalities / Appendix C：
Continua and limits Appendix E. On sums of Lp spaces / Appendix D：
A remark on parabolic equations / Appendix F：
Bibliography of Volumes 1 and 2 Erratum (Volume 1)
Index
Preface
Presentation of the models / 1：
Incompressible Models / Part 1：
Density-dependent Navier-Stokes equations / 2：
Navier-Stokes equations / 3：
Euler equations and other incompressible models / 4：
Truncation of divergence-free vectorfields
Two facts on D1,2(R2)
Compactness in time with values in weak topologies
Weak L1 estimates for solutions of the heat equation
A short proof of the existence of renormalized solutions for parabolic equations / Appendix E：
Intended Table of Contents of Volume 2
Compressible Models
Compactness results for compressible isentropic Navier-Stokes
Existence results
Related questions
Asymptotic limites / Part 3：
Asymptotic limits / 9：
Compressible models / Part 2：
Compactness results for compressible isentropic Navier-Stokes equations / 5：
Stationary problems / 6：
10.

図書
図書
10. Designs and finite geometries
edited by Dieter Jungnickel
出版情報: Boston, Mass : Kluwer Academic, 1996  254 p. ; 25 cm
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