Jorgensen, Palle E. T., Merrill, Kathy D., Packer, Judith A. (Eds.)
2008, XL, 324p. 22 illus..
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Contributed volume comprised of the work of prominent researchers
Discusses both theoretical and applied harmonic analysis including wavelets and frames
Includes recent applications to problems in sampling theory and image compression
Offers insight into some recent applications, including signal and image processing
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.
Content Level »Research
Keywords »Gelfand pair - Interpolation - Symbol - communication - harmonic analysis - image processing - signal analysis
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.-Part I. Classical and Abstract Harmonic Analysis.- Some Riemann Sums are Better than Others by V.W. Guillemin and D.W. Stroock.-Gelfand Pairs Associated with Finite Heisenberg Groups by C. Benson and G. Ratcliff.-Groups with Atomic Regular Representation by K.F. Taylor.-Wavelet Transforms and Admissible Group Representations by E. Weber.-Part II: Frames and Multiresolution Structures.-The Density Theorem and the Homogeneous Approximation Property for Gabor Frames by C. Heil.-Recent Developments on Dual Wavelet Frames by B. Han.-Characteristic Wavelet Equations and Generalizations of the Spectral Function by V. Furst.-Baggett’s Problem for Frame Wavelets by M. Bownik.-Part III: Wavelet Sets.-Simple Wavelet Sets for Scalar Dilations in R2 by K.D. Merrill.-Interpolation Maps and Congruence Domains for Wavelet Sets by X. Zhang and D.R. Larson.-Part IV: Applications to Dynamical Systems and C*-Algebras.-Orthogonal Exponentials for Bernoulli Iterated Function Systems by P.E.T. Jorgensen, K. Kornelson, and K. Shuman.-A Survey of Projective Multiresolution Analyses and a Projective Multiresolution Analysis Corresponding to the Quincunx Lattice by J.A. Packer.-Part V: Signal and Image Processing.-Sampling and Time-Frequency Localization of Bandlimited and Multiband Signals by J.A. Hogan and J.D. Lakey.-Entropy Encoding in Wavelet Image Compression by M.-S. Song.-Symbols.-Index.