Wavelet analysis : twenty years' developments : proceedings of the International Conference of Computational Harmonic Analysis : Hong Kong, China, 4-8 June 2001 / editor, Ding-Xuan Zhou.

Format:

Book

Conference/Event

Author/Creator:

International Conference of Computational Harmonic Analysis, Corporate Author.

Contributor:

Zhou, Ding-Xuan.

Conference Name:

International Conference of Computational Harmonic Analysis (2001 : Hong Kong, China)

International Conference of Computational Harmonic Analysis

Series:

Series in Analysis

Series in analysis ; v. 1

Language:

English

Subjects (All):

Wavelets (Mathematics)--Congresses.

Wavelets (Mathematics).

Harmonic analysis--Congresses.

Harmonic analysis.

Physical Description:

1 online resource (320 p.)

Place of Publication:

[River Edge], NJ : World Scientific, c2002.

Language Note:

English

Summary:

The International Conference of Computational Harmonic Analysis, held in Hong Kong during the period of June 4 - 8, 2001, brought together mathematicians and engineers interested in the computational aspects of harmonic analysis. Plenary speakers include W Dahmen, R Q Jia, P W Jones, K S Lau, S L Lee, S Smale, J Smoller, G Strang, M Vetterlli, and M V Wickerhauser. The central theme was wavelet analysis in the broadest sense, covering time-frequency and time-scale analysis, filter banks, fast numerical computations, spline methods, multiscale algorithms, approximation theory, signal processing

Contents:

Preface; Contents; Non-uniform Sampling: Exact Reconstruction from Non-uniformly Distributed Weighted-averages; 1. Introduction; 2. Wiener Amalgam Spaces; 3. AP Algorithm for Exact Reconstruction from Weighted-averages; Squeezable Bases and Semi-regular Multiresolutions; 1. Introduction; 2. Refinability; 3. Smoothness and Polynomial Reproduction; 4. Semi-regular Multiresolutions and Density; Multilevel Structure of NURBS and Formulation of NURBlets; 1. Introduction; 2. NURBS Multilevel Structure; 3. The Notion of NURBlets; 4. Decomposition and Reconstruction Matrices

5. A Demonstrative ExampleAdaptive Wavelet Methods - Basic Concepts and Applications to the Stokes Problem; 1. Introduction; 2. Variational Problems; 3. Objectives; 4. The Basic Paradigm; 5. An Equivalent l2-Problem; 6. Realization of RES; 7. Convergence Estimates; 8. Approximation Properties and Regularity - When does Adaptivity Pay?; 9. Application to the Stokes Problem; 10. Numerical Experiments; Nonstationary Wavelets; 1. Introduction; 2. Superfunction Wavelets; 3. Cascade Wavelets; 4. Approximation Properties; Spline-type Spaces in Gabor Analysis; 1. Introduction

2. Notations and Basic Facts3. Spline-type Spaces over LCA Groups; 4. Basic Facts about Weyl-Heisenberg Families; 5. Gabor Multipliers and Spline-type Spaces; Spectrum of Transition, Subdivision and Multiscale Operators; 1. Introduction; 2. Transition Operators; 3. Subdivision Operators; 4. Scaling Operators; 5. Conjugate Scaling Operators and Biorthogonality; 6. Multiscale Operators; Biorthogonal Refinable Functions and Wavelets from Spaces Generalising Splines; 1. Introduction; 2. Refinable Functions; 3. Wavelets; The Initial Functions in a Cascade Algorithm; 1. Introduction

2. Relations Among the Initial Functions in a Cascade Algorithm3. Error Estimate of a Cascade Algorithm in a Sobolev Space; On the Self-affine Sets and the Scaling Functions; 1. Introduction; 2. Self-affine Tiles; 3. Self-affine Regions; 4. Invariant Probability Measures; Cascade Algorithms in Wavelet Analysis; 1. Introduction; 2. Convergence of Cascade Algorithms; 3. Applications to Wavelet Analysis; 4. Biorthogonal Wavelet Bases; 5. Multivariate Refinable Functions; Methods for Constructing Nonseparable Compactly Supported Orthonormal Wavelets; 1. Introduction

2. Methods for Nonseparable Wavelets3. Numerical Experiments with Nonseparable Wavelets; On Some Quantum and Analytical Properties of Fractional Fourier Transforms; 1. Introduction; 2. Quantization and Periodicity; 3. Rotation, Lowering, and Raising; 4. Reduction of Orders by FrFT; 6. The Integral Representation and Properties; Block Tridiagonal Matrices and the Kalman Filter; 1. Introduction; 2. The Diagonal Entries of T-1; 3. Dynamic Least Squares and the Kalman Filter; 4. The Complete System Ax=b-e; 5. Static and Dynamic Updates; 6. The Matrix Inversion Lemma

7. Tree Structures and Kalman Filters

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

9786611929275

9781281929273

1281929271

9789812776679

9812776672