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1.

図書

図書
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
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
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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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
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
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
Martin Aigner
出版情報: Berlin ; New York : Springer, c1997  viii, 483 p. ; 24 cm
シリーズ名: Classics in mathematics
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7.

図書

図書
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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8.

図書

図書
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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9.

図書

図書
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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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:
10.

図書

図書
S. Agaian, J. Astola, K. Egiazarian
出版情報: New York : Dekker, c1995  xix, 302 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 191
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Preface
List of Symbols and Abbreviations
Introduction
Binary Polynomial Transforms / I:
Binary Polynomial Arithmetical and Logical Functions and Matrices / 1:
Rademacher Functions and Matrices / 1.1:
Arithmetical and Logical Binary Polynomial Functions. Constructions Using One Binary Operation / 1.3:
Walsh functions and matrices / 1.3.1:
Polynomial logical functions and matrices / 1.3.2:
Binary Polynomial Logical Functions and Matrices. Constructions Using Two Operations / 1.4:
Binary Polynomial Logical Functions and Matrices. Extensions of Dimension / 1.5:
Interval splicing matrices / 1.5.1:
Interval absorbing matrices / 1.5.2:
Fast Algorithms and Complexity of Binary Polynomial Transforms / 2:
General Approach to the Fast Algorithms of Binary Polynomial Transforms / 2.1:
Fast Rademacher Transforms / 2.3:
Fast Walsh Transforms / 2.4:
Fast Conjunctive Transforms / 2.5:
Fast Interval Transforms / 2.6:
Fast Disjunctive-Conjunctive Transforms / 2.7:
Lower Bounds of the Complexity of Some Binary Polynomial Transforms / 2.8:
Logical Correlations and Binary Polynomial Transforms / 3:
Arithmetical and Logical Correlation Functions / 3.1:
Arithmetical auto- and cross-correlation functions / 3.2.1:
Logical auto- and cross-correlation functions / 3.2.2:
Relations between the arithmetical and logical auto-correlation functions / 3.2.3:
General Auto- and Cross-Correlation Functions / 3.3:
Definitions / 3.3.1:
Properties of logical [rho]-correlation / 3.3.2:
Transform Method for Computation of Cross-Correlation / 3.4:
Computation of general cross-correlation / 3.4.1:
Computation of logical cross-correlation based on any Boolean operation / 3.4.2:
Power-Spectrum and General Wiener-Khinchine Theorem / 3.5:
Comments / 3.6:
Binary Polynomial Transforms and Digital Logic / II:
Spectral Methods in Analysis of Boolean Functions / 4:
Linear Boolean Functions / 4.1:
Positive (Monotone) Boolean Functions / 4.3:
Selfdual Boolean Functions / 4.4:
Symmetric Boolean Functions / 4.5:
Analysis of Fictitious Variables / 4.6:
Partial Derivatives of Boolean Functions / 4.7:
Activities of the Variables of Boolean Functions / 4.8:
Chow parameters and weighted Chow parameters of a Boolean function / 4.8.1:
Transfer from One Normal Form to Another and the Logical Operations over the Normal Forms / 4.9:
Connections between normal forms of Boolean functions / 4.9.1:
Logical operations over normal forms / 4.9.2:
Spectral Methods in Minimization of Boolean Functions / 5:
General Spectral Algorithms for Construction of the Abbreviated Disjunctive and Conjunctive Normal Forms of Boolean Function / 5.1:
Deadlock Tests and Abbreviated Normal Forms of Boolean Functions / 5.3:
Unconditional deadlock tests for tables / 5.3.1:
Abbreviated disjunctive and conjunctive normal forms of Boolean functions with a small number of ones (zeros) / 5.3.2:
Deadlock and Minimal Disjunctive and Conjunctive Normal Forms of Boolean Functions / 5.4:
Minimization of Positive (Monotone) Boolean Functions / 5.5:
Minimal disjunctive and conjunctive normal forms of positive Boolean functions / 5.5.1:
Minimization of the dual of a positive Boolean function / 5.5.2:
Quasi-Minimization of Boolean Functions / 5.6:
Reed-Muller Polynomials of Boolean Functions / 5.7:
Spectral approach to the construction of Reed-Muller polynomials / 5.7.1:
Spectral approach to generalized Reed-Muller polynomials construction / 5.7.2:
Applications in Nonlinear Digital Filtering / 5.8:
Median and Order Statistic Filters / 6:
Standard Median and Order Statistic Filters / 6.1:
Standard median filters in real domain / 6.2.1:
Standard median filters in binary domain / 6.2.2:
Standard median filters in complex domain / 6.2.3:
Order statistic filters / 6.2.4:
Two-dimensional median and order statistic filters / 6.2.5:
Histogram-type Algorithms of Fast Median and Order Statistic Filtering / 6.3:
Radix algorithms for finding median and order statistics / 6.3.1:
Histogram-type algorithms for one-dimensional running median and order statistic filtering / 6.3.2:
Histogram-type algorithms for two-dimensional running median and order statistic filtering / 6.3.3:
Decomposition Algorithms of Median and Order Statistic Filtering / 6.4:
Decomposition algorithms for finding median and order statistic / 6.4.1:
Decompositional algorithms for running median and order statistic filtering / 6.4.2:
Weighted Order Statistic and Stack Filters / 7:
Weighted Median and Weighted Order Statistic Filters / 7.1:
Weighted median filters in the real domain / 7.1.1:
Weighted median filters in binary domain / 7.1.2:
Weighted median filters in complex domain / 7.1.3:
Weighted order statistic filters / 7.1.4:
Histogram-Type Algorithms for Finding Weighted Order Statistics / 7.2:
Histogram-Type Algorithms for Running Weighted Order Statistic Filtering / 7.3:
Running algorithm for linearly distributed weights / 7.3.1:
Running algorithm for exponentially distributed weights / 7.3.2:
Running algorithm for combination of weights / 7.3.3:
Histogram-type algorithms for two-dimensional running weighted order statistic filtering / 7.3.4:
Decomposition Algorithms of Weighted Order Statistic Filtering / 7.4:
Stack Filters / 7.5:
Stack Filters and Threshold Decomposition / 7.5.1:
Decomposition Methods for Stack Filtering / 7.6:
Decomposition methods of stack filtering for fixed window / 7.6.1:
Decomposition methods of stack filtering for running window / 7.6.2:
Spectral Approach to Stack and Weighted Order Statistic Filters / 7.7:
Statistical Properties of Stack Filters / 8:
Noise Attenuation for Order Statistics / 8.1:
Maximum Likelihood Estimators / 8.3:
Output Distribution Functions of Weighted Order Statistic and Stack Filters / 8.4:
Output distribution functions of a stack filter / 8.4.1:
Output distribution function of a weighted order statistic filter / 8.4.2:
Joint Distributions of Stack Filters / 8.5:
Definitions and notations / 8.5.1:
Joint cumulative distribution of L stack filters / 8.5.2:
Spectral Approach to the Calculation of the Joint Distribution of Stack Filters / 8.6:
Selection Probabilities of Stack Filters / 8.7:
Definitions and properties / 8.7.1:
Selection probabilities of weighted order statistic filters / 8.7.2:
Partial derivatives of PBF and selection probability sets of stack filters / 8.7.3:
Activities of variables of Boolean functions and the combination matrix of continuous stack filters / 8.7.4:
Weighted activities of variables and joint selection probability matrix of stack filters / 8.7.5:
Sample selection probability vectors and weighted Chow parameters / 8.7.6:
Spectral Approach to the Calculation of Selection Probabilities / 8.8:
Construction of selection probability sets for continuous stack filters / 8.8.1:
Construction of joint selection probability matrix for continuous stack and WOS filters / 8.8.2:
Construction of sample selection probability vector for continuous stack filters / 8.8.3:
Construction of rank selection probability vector for continuous stack filters / 8.8.4:
Index / 8.9:
Preface
List of Symbols and Abbreviations
Introduction
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