Generalized harmonic analysis and wavelet packets

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Generalized harmonic analysis and wavelet packets / Khalifa Trimèche

資料種別:: 図書
出版情報:: Amsterdam : Gordon & Breach Science Publishers, c2001
形態:: xii, 306 p. ; 26 cm
著者名:: Trimèche, K <DA03274363>
ISBN:: 9789056993290 [9056993291]
書誌ID:: BA54701680

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注記:

Includes bibliographical references (p. [293]-302) and index

言語:

英語

目次情報:

Introduction

The Normalized Bessel Function Of First Kind / 1：

The Bessel function of first kind / 1.I.：

Definition / 1.I.1.：

Derivatives and differential equation of the Bessel function J[subscript v] / 1.I.2.：

Asymptotic formulas for the Bessel function J[subscript v] / 1.I.3.：

The Poisson integral representations of the Bessel function J[subscript v] / 1.I.4.：

The Sonine's first integral for the Bessel functions J[subscript alpha] and J[subscript beta] / 1.I.5.：

Addition formulas for the Bessel function J[subscript v] / 1.I.6.：

Product formulas for the Bessel function J[subscript v] / 1.I.7.：

The normalized Bessel function of first kind / 1.II.：

Properties of the function j[subscript alpha] ([lambda]x) / 1.II.1.：

Integral representations of the function j[subscript alpha] ([lambda]x) / 1.II.3.：

The Poisson integral representations / 1.II.3.a.：

The Sonine's first integral / 1.II.3.b.：

Product formula for the function j[subscript alpha] / 1.II.4.：

Useful formulas involving the function j[subscript alpha] / 1.II.5.：

Problems / 1.III.：

Riemann-Liouville And Weyl Integral Transforms / 2：

The Riemann-Liouville integral transform / 2.I.：

Definition and properties / 2.I.1.：

Inversion of the operator R[subscript alpha] / 2.I.2.：

The Riemann-Liouville integral transform on the spaces L[superscript p]([0, + [infinity][, dx), 1[less than or equal]p[less than or equal]+[infinity] / 2.I.3.：

The Weyl integral transform / 2.II.：

Inversion of the operator W[subscript alpha] / 2.II.1.：

The Weyl integral transform on the space and[subscript *](IR) / 2.III.：

The Weyl transform on the space E'[subscript *](IR) / 2.IV.：

The Sonine integral transform and its dual / 2.V.：

The Sonine integral transform / 2.V.1.：

The Sonine integral transform on the spaces L[superscript p]([0, + [infinity][, dx], 1[less than or equal]p[less than or equal]+[infinity] / 2.V.2.：

The dual Sonine integral transform / 2.V.3.：

The Sonine transform on the space E'[subscript *](IR) / 2.V.4.：

Convolution Product And Fourier-Cosine Transform Of Functions, Measures And Distributions / 2.VI.：

Convolution product of functions and distributions / 3.I.：

The translation operator / 3.I.1.：

Convolution product of functions / 3.I.2.：

Convolution product of measures / 3.I.3.：

Convolution product of distributions / 3.I.4.：

The Fourier-cosine transform / 3.II.：

The Fourier-cosine transform on L[superscript 1]([0, +[infinity][, dx) / 3.II.1.：

The Fourier-cosine transform on and[subscript *](IR) and D[subscript *](IR) / 3.II.2.：

The Fourier-cosine transform on L[superscript 2]([0, +[infinity][, dx) / 3.II.3.：

The Fourier-cosine transform on M[superscript b]([0, +[infinity][) / 3.II.4.：

The Fourier-cosine transform on E'[subscript *](IR) and and'[subscript *](IR) / 3.II.5.：

Generalized Convolution Product Associated With The Bessel Operator / 3.III.：

Convolution product of radial functions / 4.I.：

Convolution product / 4.I.1.：

Generalized translation operators associated with the Bessel operator / 4.II.：

Generalized convolution product associated with the Bessel operator / 4.III.：

Generalized convolution product of functions / 4.III.1.：

Generalized convolution product of measures of M[superscript b]([0,+[infinity][) / 4.III.2.：

Generalized convolution product of distributions / 4.III.3：

Fourier-Bessel Transform / 4.IV.：

Fourier transform of radial functions / 5.I.：

The Fourier-Bessel transform on L[superscript 1]([0, + [infinity][, d[mu subscript alpha]) / 5.II.：

The Fourier-Bessel transform on and[subscript *](IR) and D[subscript *](IR) / 5.III.：

The Fourier-Bessel transform on L[superscript 2]([0, + [infinity][, d[mu subscript alpha]) / 5.IV.：

The Fourier-Bessel transform on L[superscript p]([0, + [infinity][, d[mu subscript alpha]),1[less than or equal]p[less than or equal]2 / 5.V.：

The Fourier-Bessel transform on M[superscript b]([0, + [infinity][) / 5.VI.：

The Fourier-Bessel transform on E'[subscript *](IR) and and'[subscript *](IR) / 5.VII.：

Infinitely Divisible Probabilities And Central Limit Theorem Associated With The Bessel Operator / 5.VIII.：

Dispersion of a probability measure on [0, + [infinity][ / 6.I.：

Generalized quadratic form / 6.I.1.：

Levy's theorem / 6.I.2.：

Levy-Khintchine's formula / 6.II.：

Convolution semigroups and infinitely divisible probabilities associated with the Bessel operator / 6.III.：

Convolution semigroups / 6.III.1.：

Infinitely divisible probabilities associated with the Bessel operator / 6.III.2.：

Central limit theorem associated with the Bessel operator / 6.IV.：

Continuous Wavelet Transform Associated With The Bessel Operator / 7：

Classical continuous wavelet transform on [0, + [infinity][ / 7.I.：

Classical wavelets on [0, + [infinity][ / 7.I.1.：

Continuous wavelet transform associated with the Bessel operator / 7.I.2.：

Wavelets associated with the Bessel operator / 7.II.1.：

Continuous wavelet transform associated, with the Bessel operator / 7.II.2.：

Inversion formulas for the operator R[subscript alpha] and W[subscript alpha] / 7.III.：

Inversion formulas for the operators R[subscript alpha] and W[subscript alpha] using wavelets associated with the Bessel operator / 7.IV.：

Wavelet Packets Associated With The Bessel Operator / 7.V.：

The P-wavelet packet transform associated with the Bessel operator / 8.I.：

Plancherel and reconstruction formulas / 8.I.1.：

Calderon's reproducing formula / 8.I.2：

Scale discrete scaling function associated with the Bessel operator / 8.II.：

Modified packet associated with the Bessel operator / 8.III.：

S-wavelet packet associated with the Bessel operator / 8.IV.：

Multiresolution analysis by means of wavelet packets associated with the Bessel operator / 8.V.：

Continuous Linear Wavelet Transform Associated With The Bessel Operator And Its Discretization / 8.VI.：

Linear wavelets associated with the Bessel operator / 9.I.：

Linear wavelet packets associated with the Bessel operator / 9.II.：

Scale discrete L-scaling function associated with the Bessel operator / 9.III.：

Bibliography

Index

Introduction

The Normalized Bessel Function Of First Kind / 1：

The Bessel function of first kind / 1.I.：

Definition / 1.I.1.：

Derivatives and differential equation of the Bessel function J[subscript v] / 1.I.2.：

Asymptotic formulas for the Bessel function J[subscript v] / 1.I.3.：

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