Advances in Gabor Analysis

1. Front Matter

   Pages i-xix

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2. Introduction

   • Hans G. Feichtinger, Thomas Strohmer

   Pages 1-9

3. Uncertainty Principles for Time-Frequency Representations

   • Karlheinz Gröchenig

   Pages 11-30

4. Zak Transforms with Few Zeros and the Tie

   • A. J. E. M. Janssen

   Pages 31-70

5. Bracket Products for Weyl—Heisenberg Frames

   • Peter G. Casazza, Mark C. Lammers

   Pages 71-98

6. A First Survey of Gabor Multipliers

   • Hans G. Feichtinger, Krzysztof Nowak

   Pages 99-128

7. Aspects of Gabor Analysis and Operator Algebras

   • Jean-Pierre Gabardo, Deguang Han

   Pages 129-152

8. Integral Operators, Pseudodifferential Operators, and Gabor Frames

   • Christopher Heil

   Pages 153-169

9. Methods for Approximation of the Inverse (Gabor) Frame Operator

   • Ole Christensen, Thomas Strohmer

   Pages 171-195

10. Wilson Bases on the Interval

    • Kai Bittner

    Pages 197-221

11. Localization Properties and Wavelet-Like Orthonormal Bases for the Lowest Landau Level

    • Jean-Pierre Antoine, Fabio Bagarello

    Pages 223-258

12. Optimal Stochastic Encoding and Approximation Schemes using Weyl—Heisenberg Sets

    • Radu Balan, Ingrid Daubechies

    Pages 259-320

13. Orthogonal Frequency Division Multiplexing Based on Offset QAM

    • Helmut Bölcskei

    Pages 321-352

14. Back Matter

    Pages 353-356

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The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the engineering, mathematical, and scientific communities with significant developments in harmonic analysis, ranging from abstract har­ monic analysis to basic applications. The title of the series reflects the im­ portance of applications and numerical implementation, but richness and relevance of applications and implementation depend fundamentally on the structure and depth of theoretical underpinnings. Thus, from our point of view, the interleaving of theory and applications and their creative symbi­ otic evolution is axiomatic. Harmonic analysis is a wellspring of ideas and applicability that has flour­ ished, developed, and deepened over time within many disciplines and by means of creative cross-fertilization with diverse areas. The intricate and fundamental relationship between harmonic analysis and fields such as sig­ nal processing, partial differential equations (PDEs), and image processing is reflected in our state of the art ANHA series. Our vision of modern harmonic analysis includes mathematical areas such as wavelet theory, Banach algebras, classical Fourier analysis, time­ frequency analysis, and fractal geometry, as well as the diverse topics that impinge on them.

• Potential
• Signal
• algorithms
• communication
• electrical engineering
• harmonic analysis
• image processing
• numerical analysis

"The authors have put their effort into writing articles with the necessary background to make their presentations attractive and including a complete set of references. Good introductions and detailed expositions of ideas are given in all the presentations. These features make this book an invaluable tool for researchers interested in signal analysis. The research community will benefit greatly from this publication." —Mathematical Reviews

"The present book can be considered as a continuation of two previous ones: Gabor Analysis and Algorithms: Theory and Applications, H. G. Feichtinger and T. Strohmer, Eds., Birkhäuser 1998, and the book by K. Gröchenig, Foundations of Time-Frequency Analysis, Birkhäuser 2001. It contains survey chapters, but new results that have not been published previously are also included. The introductory chapter of the book, written by H. G. Feichtinger and T. Strohmer, contains a clear outline of the contents as well as some comments on the future developments in Gabor analysis.

Written by leading experts in the field, the volume appeals, by its interdisciplinary character, to a large audience, both novices and experts, theoretically inclined researchers and practitioners as well. It brilliantly illustrates how application areas and pure and applied mathematics can work together with profit for all." —Revue D'Analyse Numérique et de Théorie de L'Approximation, 2004

"A mathematically sound and self-contained presentation on recent advances in the highly applicable field of Gabor analysis.… This book is a must for all interested in signal analysis, and, of course, in particular in Gabor analysis." —Monatschefte für Mathematik

 

• Department of Mathematics, University of Vienna, Vienna, Austria

  Hans G. Feichtinger

• Department of Mathematics, University of California—Davis, Davis, USA

  Thomas Strohmer

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