eBook ISBN:  9781470402297 
Product Code:  MEMO/134/640.E 
List Price:  $45.00 
MAA Member Price:  $40.50 
AMS Member Price:  $27.00 
eBook ISBN:  9781470402297 
Product Code:  MEMO/134/640.E 
List Price:  $45.00 
MAA Member Price:  $40.50 
AMS Member Price:  $27.00 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 134; 1998; 68 ppMSC: Primary 46; 47
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.
ReadershipResearch mathematicians, engineers and graduate students interested in functional analysis and/or wavelet theory; computer scientsts.

Table of Contents

Chapters

Introduction

1. The local commutant

2. Structural theorems

3. The wavelet system ($D$, $T$)

4. Wavelet sets

5. Operator interpolation of wavelets

6. Concluding remarks


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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.
Research mathematicians, engineers and graduate students interested in functional analysis and/or wavelet theory; computer scientsts.

Chapters

Introduction

1. The local commutant

2. Structural theorems

3. The wavelet system ($D$, $T$)

4. Wavelet sets

5. Operator interpolation of wavelets

6. Concluding remarks