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Memoirs of the American Mathematical Society
1998; 68 pp; softcover
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.
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.
Research mathematicians, engineers and graduate students interested in functional analysis and/or wavelet theory; computer scientsts.
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