Memoirs of the American Mathematical Society 1998; 68 pp; softcover Volume: 134 ISBN10: 0821808001 ISBN13: 9780821808009 List Price: US$42 Individual Members: US$25.20 Institutional Members: US$33.60 Order Code: MEMO/134/640
 This volume concerns some general methods for the analysis of those orthonormal bases for a separable complex infinite dimensional Hilbert space which are generated by the action of a system of unitary transformations on a single vector, which is called a complete wandering vector for the system. The main examples are the orthonormal wavelet bases. Topological and structural properties of the set of all orthonormal dyadic wavelets are investigated in this way by viewing them as complete wandering vectors for an affiliated unitary system and then applying techniques of operator algebra and operator theory. Features:  describes an operatortheoretic perspective on wavelet theory that is accessible to functional analysts
 describes some natural generalizations of standard wavelet systems
 contains numerous examples of computationally elementary wavelets
 poses many open questions and directions for further research
This book is particularly accessible to operator theorists and operator algebraists who are interested in a functional analytic approach to some of the pure mathematics underlying wavelet theory. Readership Research mathematicians, engineers and graduate students interested in functional analysis and/or wavelet theory; computer scientsts. Table of Contents  Introduction
 The local commutant
 Structural theorems
 The wavelet system \(\langle D,T\rangle\)
 Wavelet sets
 Operator interpolation of wavelets
 Concluding remarks
 Appendix: Examples of interpolation maps
 Bibliography
