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Harmonic Analysis and Applications : In Honor of John J. Benedetto - Christopher Heil

Harmonic Analysis and Applications

In Honor of John J. Benedetto

By: Christopher Heil (Editor)


Published: 1st May 2006
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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

Forewordp. vii
Prefacep. xi
The Benedetto Mathematical Family Treep. xv
Publications of John J. Benedettop. xvii
Harmonic Analysis
The Gibbs Phenomenon in Higher Dimensionsp. 3
Weighted Sobolev Inequalities for Gradientsp. 17
Semidiscrete Multipliersp. 25
Frame Theory
A Physical Interpretation of Tight Framesp. 51
Time-Frequency Analysis
Recent Developments in the Balian-Low Theoremp. 79
Some Problems Related to the Distributional Zak Transformp. 101
Gabor Duality Characterizationsp. 127
A Pedestrian's Approach to Pseudodifferential Operatorsp. 139
Linear Independence of Finite Gabor Systemsp. 171
Wavelet Theory
Explicit Cross-Sections of Singly Generated Group Actionsp. 209
The Theory of Wavelets with Composite Dilationsp. 231
Sampling Theory and Shift-Invariant Spaces
Periodic Nonuniform Sampling in Shift-Invariant Spacesp. 253
Sampling on Unions of Shifted Lattices in One Dimensionp. 289
Learning the Right Model from the Datap. 325
Redundancy in the Frequency Domainp. 335
Density Results for Frames of Exponentialsp. 359
Indexp. 371
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780817637781
ISBN-10: 0817637788
Series: Applied and Numerical Harmonic Analysis
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 374
Published: 1st May 2006
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 2.54
Weight (kg): 1.65