Palle E T Jorgensen

Representations, Wavelets, and Frames: A Celebration of the Mathematical Work of Lawrence W. Baggett - Applied and Numerical Harmonic Analysis Palle E T Jorgensen 2008 edition

Marc Notes: Includes bibliographical references and index. Jacket Description/Back: Motivated by applications, an underlying theme in analysis is that of finding bases and understanding the transforms that implement them. These may be based on Fourier techniques or involve wavelet tools; they may be orthogonal or have redundancies (e.g., frames from signal analysis). Representations, Wavelets, and Frames contains chapters pertaining to this theme from experts and expositors of renown in mathematical analysis and representation theory. Topics are selected with an emphasis on fundamental and timeless techniques with a geometric and spectral-theoretic flavor. The material is self-contained and presented in a pedagogical style that is accessible to students from both pure and applied mathematics while also of interest to engineers. The book is organized into five sections that move from the theoretical underpinnings of the subject, through geometric connections to tilings, lattices and fractals, and concludes with analyses of computational schemes used in communications engineering. Within each section, individual chapters present new research, provide relevant background material, and point to new trends and open questions. Contributors: C. Benson, M. Bownik, V. Furst, V. W. Guillemin, B. Han, C. Heil, J. A. Hogan, P. E. T. Jorgensen, K. Kornelson, J. D. Lakey, D. R. Larson, K. D. Merrill, J. A. Packer, G. Ratcliff, K. Shuman, M.-S. Song, D. W. Stroock, K. F. Taylor, E. Weber, X. Zhang. Description for Sales People: Representations, Wavelets, and Frames contains chapters pertaining to this theme from experts and expositors of renown in mathematical analysis and representation theory. Topics are selected with an emphasis on fundamental and timeless techniques with a geometric and spectral-theoretic flavor. The material is self-contained and presented in a pedagogical style that is accessible to students from both pure and applied mathematics while also of interest to engineers. Table of Contents: ANHA Series Preface -- Foreword -- Preface -- Acknowledgments -- Mathematical Family Tree of Lawrence W. Baggett -- Publications of Lawrence W. Baggett -- Co-workers of Lawrence W. Baggett -- Titles of All Talks -- I. Classical and Abstract Harmonic Analysis -- 1. Some Riemann Sums Are Better Than Others / Victor W. Guillemin, Daniel W. Stroock -- 2. Gelfand Pairs Associated with Finite Heisenberg Groups / Chal Benson, Gail Ratcliff -- 3. Groups with Atomic Regular Representation / Keith F. Taylor -- 4. Wavelet Transforms and Admissible Group Representations / Eric Weber -- II. Frames and Multiresolution Structures -- 5. The Density Theorem and the Homogeneous Approximation Property for Gabor Frames / Christopher Heil -- 6. Recent Developments on Dual Wavelet Frames / Bin Han -- 7. Characteristic Wavelet Equations and Generalizations of the Spectral Function / Veronika Furst -- 8. Baggett's Problem for Frame Wavelets / Marcin Bownik -- III. Wavelet Sets -- 9. Simple Wavelet Sets for Scalar Dilations in R[superscript 2] / Kathy D. Merrill -- 10. Interpolation Maps and Congruence Domains for Wavelet Sets / Xiaofei Zhang, David R. Larson -- IV. Applications to Dynamical Systems and C*-Algebras -- 11. Orthogonal Exponentials for Bernoulli Iterated Function Systems / Palle E. T. Jorgensen, Keri Kornelson, Karen Shuman -- 12. A Survey of Projective Multiresolution Analyses and a Projective Multiresolution Analysis Corresponding to the Quincunx Lattice / Judith A. Packer -- V. Signal and Image Processing -- 13. Sampling and Time-Frequency Localization of Band-Limited and Multiband Signals / Jeffrey A. Hogan, Joseph D. Lakey -- 14. Entropy Encoding in Wavelet Image Compression / Myung-Sin Song -- Symbols -- Index. Publisher Marketing: The work of Lawrence Baggett has had a profound impact on the field of abstract harmonic analysis and the many areas of mathematics that use its techniques. Contributions in this volume reflect this broad scope, and Larry's unusual ability to bring together techniques from disparate fields.