20% Discount Pre-Pub Offer Forthcoming June 2002! List Price: $59.95 (tent.) Special Price: $47.96 + shipping & handling Wavelets through a Please mention reference # Y404 when placing your order! Offer Valid Until 31 August 2002 Looking Glass Table of Contents The World of the Spectrum List of Figures List of Tables O. Bratteli, University of Oslo, Oslo, Norway Preface P. Jorgensen, University of Iowa, Iowa City, IA 1. Introduction Overture: Why wavelets? * Subband filters This book combining wavelets and the world of the spectrum focuses on recent and sieves * Matrix functions and developments in wavelet theory, emphasizing fundamental and relatively multiresolutions * Qubits: The oracle of timeless techniques that have a geometric and spectral-theoretic flavor. The Feynman and the algorithm of Shor * Chaos exposition is clearly motivated and unfolds systematically, aided by numerous and cascade approximation * Spectral bounds for the transfer and subdivision graphics. operators * Connections to group theory * Wavelet packets * The Gabor transform * Key features of the book: Exercises * Terminology 2. Homotopy Theory and Cascades • The important role of the spectrum of a transfer operator is studied The dangers of navigating the landscape of • wavelets * Homotopy classes of wavelets * Excellent graphics show how wavelets depend on the spectra of the transfer Multiresolution analysis and tight frames * operators Generality of multiresolution analysis * • Key topics of wavelet theory are examined: connected components in the Global homotopy and an index theorem * Cascades in L2(R) * An open problem * variety of wavelets, the geometry of winding numbers, the Galerkin projection Exercises method, classical functions of Weierstrass and Hurwitz and their role in describing the eigenvalue-spectrum of the transfer operator, isospectral 3. Can You Hear the Shape of a Wavelet? families of wavelets, spectral radius formulas for the transfer operator, Perron– The world of the spectrum * Transfer operators * Galerkin projections and spectra Frobenius theory, and quadrature mirror filters of transfer operators * Spectrum and • New previously unpublished results appear on the homotopy of regularity * The spectra of restrictions of the multiresolutions, on approximation theory, and on the spectrum and structure transfer operator * The spectral radius * Exercises of the fixed points of the associated transfer and subdivision operators • Concise background material for each chapter, open problems, exercises, 4.TheTransferOperatorandPerron– bibliography, and comprehensive index make this work a fine pedagogical and Frobenius Theory A slanted matrix from dynamics * The duality reference resource. between kneading and chopping * A Green’s function* The Perron–Frobenius This self-contained book deals with the tools for important applications to signal eigenfunction * Approximation theory * processing, communications engineering, computer graphics algorithms, qubit Ergodic means * Exercises algorithms and chaos theory, and is aimed at a broad readership of graduate 5. The Fixed Points of the Transfer Operator students, practitioners, and researchers in applied mathematics and engineering. The fine structure of correlations *The The book is also useful for other mathematicians with an interest in the interface minimal function g such that R(g)=g,0ÿgÿ1, between mathematics and communication theory. and g(1)=1 * The C*-algebra ker (1 – R|C(T)): Estimates and identities * Inverse spectral theory * Cycles * Pure states * Historical Applied and Numerical Harmonic Analysis notes and remarks * Exercises 6. Orthogonalization and Isospectral Due June, 2002 / 424 pp., 112 illus. / Hardcover Approximation ISBN 0-8176-4280-3 The other side of wavelets *Examples* Spectral properties of biothogonal wavelets * Isospectral approximation * Biothogonal frames: Multiresolution analysis and index theorem * Exercises References Index ORDER FORM Three Easy Ways to Order 20% Discount Pre-Pub Offer Call: 1-800-777-4643 (within North & South America) List Price: $59.95 (tent.) (212) 460-1500 (outside North & South America) Fax: (201) 348-4505 Special Price: $47.96 + shipping & handling Mail: Birkhäuser, PO Box 2485 Please mention reference # Y404 when Secaucus, NJ 07096-2485 placing your order! Offer Valid Until 31 August 2002 YES, Please send me Wavelets through a Looking Glass: SATISFACTION GUARANTEED! The World of the Spectrum Remember: Your 30-Day return privilege By O. Bratteli and P. Jorgensen, ISBN 0-8176-4280-3 is always Guaranteed! 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