Advances in Gabor Analysis

This unified, self-contained volume provides insight into the richness of Gabor analysis and its potential for future development in applied mathematics and engineering. Mathematicians and engineers treat a range of topics covering theory as well as applications in eleven survey chapters. Taken as a whole, the work demonstrates interactions and connections among different areas in which Gabor analysis plays a critical role, including harmonic analysis, operator theory, quantum physics, numerical analysis, electrical engineering, and signal/image processing.§Key features of the work:§Gives an overview of recent developments in Gabor analysis, an important tool in the understanding and use of time-frequency analysis methods in a variety of disciplines§Provides sufficient background material along with many new and previously unpublished results§Presents applications to areas such as digital and wireless communications§Up-to-date bibliographies for each chapter; useful subject index for the entire volume§Specific topics covered include: Uncertainty Principles for Time-Frequency Representations; Zak Transforms; Bracket Products for Weyl--Heisenberg Frames; Gabor Multipliers; Gabor Analysis and Operator Algebras; Integral Operators, Pseudodifferential Operators and Gabor Frames; Methods for Approximation of the Inverse (Gabor) Frame Operator; Wilson Bases§Graduate students, professionals, and researchers in pure and applied mathematics, mathematical physics, electrical and communications engineering will find Advances in Gabor Analysis a comprehensive resource.§Contributors: J.-P. Antoine, F. Bagarello, R. Balan, K. Bittner, H. Bölcskei, P.G. Casazza, O. Christensen, I. Daubechies, H.G. Feichtinger, J.-P. Gabardo, K. Gröchenig, D. Han, C. Heil, A.J.E.M. Janssen, M.C. Lammers, K. Nowak, T. Strohmer