Advances in Gabor Analysis

ISBN-13: 9781461266273 / Angielski / Miękka / 2012 / 356 str.

Hans G. Feichtinger; Thomas Strohmer; Hans G. Feichtinger

Opis

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.

Recenzje

"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

 

Spis treści

Foreword/H. Landau Contributors Introduction /H.G. Feichtinger and T. Strohmer Uncertainty Principles for Time-Frequency Representations /K. Gröchenig Zak Transforms with Few Zeros and the Tie /A.J.E.M Janssen Bracket Products for Weyl--Heisenberg Frames /P.G. Casazza and M.C. Lammers A First Survey of Gabor Multipliers /H.G. Feichtinger and K. Nowak Aspects of Gabor Analysis and Operator Algebras /J.-P. Gabardo and D. Han Integral Operators, Pseudodifferential Operators, and Gabor Frames /C. Heil Methods for Approximation of the Inverse (Gabor) Frame Operator /O. Christensen and T. Strohmer Wilson Bases on the Interval /K. Bittner Localization Properties and Wavelet-Like Orthonormal Bases for the Lowest Landau Level /J.-P. Antoine and F. Bagarello Optimal Stochastic Encoding and Approximation Schemes using Weyl--Heisenberg Sets /R. Balan and I. Daubechies Orthogonal Frequency Division Multiplexing Based on Offset QAM /H. Bölcskei Index

O autorze

Unified, self-contained volume providing insight into the richness of Gabor analysis and its potential for development in applied mathematics and engineering. Mathematicians and engineers treat a range of topics, and cover theory and applications to areas such as digital and wireless communications. The work demonstrates interactions and connections among areas in which Gabor analysis plays a role: harmonic analysis, operator theory, quantum physics, numerical analysis, signal/image processing. For graduate students, professionals, and researchers in pure and applied mathematics, math physics, and engineering.