Applied and Numerical Harmonic Analysis

In Honor of John J. Benedetto

By: Christopher Heil (Editor)

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Hardcover | 11 August 2006

At a Glance

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408 Pages

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15.88 x 24.13 x 2.54

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John J. Benedetto has had a profound influence not only on the direction of harmonic analysis and its applications, but also on the entire community of people involved in the field. This self-contained volume in honor of John covers a wide range of topics in harmonic analysis and related areas, including weighted-norm inequalities, frame theory, wavelet theory, time-frequency analysis, and sampling theory. The invited chapters pay tribute to John's many achievements and express an appreciation for both the mathematical and personal inspiration he has given to so many students, coauthors, and colleagues.

Although the scope of the book is broad, chapters are clustered by topic to provide authoritative expositions that will be of lasting interest. The original papers collected here are written by prominent, well-respected researchers and professionals in the field of harmonic analysis. The book is divided into the following five sections:

* Classical harmonic analysis

* Frame theory

* Time-frequency analysis

* Wavelet theory

* Sampling theory and shift-invariant spaces

Harmonic Analysis and Applications is an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics.

Contributors: A. Aldroubi, L. Baggett, G. Benke, C. Cabrelli, P.G. Casazza, O. Christensen, W. Czaja, M. Fickus, J.-P. Gabardo, K. Grochenig, K. Guo, E. Hayashi, C. Heil, H.P. Heinig, J.A. Hogan, J. Kovacevic, D. Labate, J.D. Lakey, D. Larson, M.T. Leon, S. Li, W.-Q Lim, A. Lindner, U. Molter, A.M. Powell, B. Rom, E. Schulz, T. Sorrells, D. Speegle, K.F. Taylor, J.C. Tremain, D. Walnut, G. Weiss, E. Wilson, G. Zimmermann

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You Can Find This Book In

Non-Fiction Mathematics Number Theory Calculus & Mathematical Analysis Complex Analysis Functional Analysis & Transforms Differential Calculus & Equations

Foreword	p. vii
Preface	p. xi
The Benedetto Mathematical Family Tree	p. xv
Publications of John J. Benedetto	p. xvii
Harmonic Analysis
The Gibbs Phenomenon in Higher Dimensions	p. 3
Weighted Sobolev Inequalities for Gradients	p. 17
Semidiscrete Multipliers	p. 25
Frame Theory
A Physical Interpretation of Tight Frames	p. 51
Time-Frequency Analysis
Recent Developments in the Balian-Low Theorem	p. 79
Some Problems Related to the Distributional Zak Transform	p. 101
Gabor Duality Characterizations	p. 127
A Pedestrian's Approach to Pseudodifferential Operators	p. 139
Linear Independence of Finite Gabor Systems	p. 171
Wavelet Theory
Explicit Cross-Sections of Singly Generated Group Actions	p. 209
The Theory of Wavelets with Composite Dilations	p. 231
Sampling Theory and Shift-Invariant Spaces
Periodic Nonuniform Sampling in Shift-Invariant Spaces	p. 253
Sampling on Unions of Shifted Lattices in One Dimension	p. 289
Learning the Right Model from the Data	p. 325
Redundancy in the Frequency Domain	p. 335
Density Results for Frames of Exponentials	p. 359
Index	p. 371
Table of Contents provided by Ingram. All Rights Reserved.

Applied and Numerical Harmonic Analysis

In Honor of John J. Benedetto

At a Glance

Hardcover

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