**Memoirs of the American Mathematical Society**

1998;
68 pp;
Softcover

MSC: Primary 46; 47;

Print ISBN: 978-0-8218-0800-9

Product Code: MEMO/134/640

List Price: $45.00

AMS Member Price: $27.00

MAA member Price: $40.50

**Electronic ISBN: 978-1-4704-0229-7
Product Code: MEMO/134/640.E**

List Price: $45.00

AMS Member Price: $27.00

MAA member Price: $40.50

# Wandering Vectors for Unitary Systems and Orthogonal Wavelets

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*Xingde Dai; David R. Larson*

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 operator-theoretic 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

# Table of Contents

## Wandering Vectors for Unitary Systems and Orthogonal Wavelets

- Contents vii8 free
- Introduction 110 free
- Chapter 1. The Local Commutant 413 free
- Chapter 2. Structural Theorems 1322
- Chapter 3. The Wavelet System (D,T) 2130
- Chapter 4. Wavelet Sets 3039
- Chapter 5. Operator Interpolation of Wavelets 3847
- Chapter 6. Concluding Remarks 5362
- Appendix: Examples of Interpolation Maps 6170
- Bibliography 6877