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9780821820674

Frames, Bases, and Group Representations

by ;
  • ISBN13:

    9780821820674

  • ISBN10:

    0821820672

  • Format: Paperback
  • Copyright: 2000-09-01
  • Publisher: Amer Mathematical Society

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Summary

We develop an operator-theoretic approach to discrete frame theory on a separable Hilbert space. We then apply this to an investigation of the structural properties of systems of unitary operators on Hilbert space which are related to orthonormal wavelet theory. We also obtain applications of frame theory to group representations, and of the theory of abstract unitary systems to frames generated by Gabor type systems.

Table of Contents

Abstract ix
Introduction 1(4)
Basic Theory for Frames
5(16)
A Dilation Viewpoint on Frames
5(9)
The Canonical Dual Frame
14(2)
Alternate Dual Frames
16(5)
Complementary Frames and Disjointness
21(18)
Strong Disjointness, Disjointness and Weak Disjointness
21(3)
Characterizations of Equivalence and Disjointness
24(5)
Cuntz Algebra Generators
29(1)
More on Alternate Duals
30(9)
Frame Vectors for Unitary Systems
39(10)
The Local Commutant and Frame Vectors
39(3)
Dilation Theorems for Frame Vectors
42(5)
Equivalence Classes of Frame Vectors
47(2)
Gabor Type Unitary Systems
49(6)
Frame Wavelets, Super-wavelets and Frame Sets
55(24)
Frame Sets
55(3)
Super-wavelets
58(7)
A Characterization of Super-wavelets
65(1)
Some Frazier-Jawerth Frames
66(4)
MRA Super-wavelets
70(3)
Interpolation Theory
73(6)
Frame Representations for Groups
79(10)
Basics
79(1)
Frame Multiplicity
80(4)
Parameterizations of Frame Vectors
84(2)
Disjoint Group Representations
86(3)
Concluding Remarks
89(1)
Spectral families of frames:
89(1)
A Joint Project with Pete Casazza
90(1)
A Matrix Completion Characterization of Frames
90(1)
Some Acknowledgements
90(1)
Density and Connectivity of Gabor Type Frames
91

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What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

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