Preface * List of Figures * List of Tables * Introduction * Homotopy Theory and Cascades * Can You Hear the Shape of a Wavelet? * The Transfer Operator and Perron-Frobenius Theory * The Fixed Points of the Transfer Operator * Orthogonalization and Isospectral Approximation * References * Index

? Concise background material for each chapter, open problems, exercises, bibliography, and comprehensive index make this work a fine pedagogical and reference resource.; New previously unpublished results appear on the homotopy of multiresolutions, approximation theory, the spectrum and structure of the fixed points of the associated transfer, subdivision operators; Key topics of wavelet theory are examined; Excellent graphics show how wavelets depend on the spectra of the transfer operators; The important role of the spectrum of a transfer operator is studied; This self-contained book deals with important applications to signal processing, communications engineering, computer graphics algorithms, qubit algorithms and chaos theory.