Advances in Gabor Analysis

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.

Contenu

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