Frames, bases, and group representations / Deguang Han, David R. Larson.

Format:

Book

Author/Creator:

Han, Deguang, 1959- author.

Larson, David R., 1942- author.

Series:

Memoirs of the American Mathematical Society ; no. 697.

Memoirs of the American Mathematical Society, 0065-9266 ; number 697

Language:

English

Subjects (All):

Frames (Vector analysis).

Operator theory.

Wavelets (Mathematics).

Representations of groups.

Physical Description:

1 online resource (111 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2000.

Language Note:

English

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.

Contents:

""Contents""; ""Abstract""; ""Introduction""; ""Chapter 1. Basic Theory for Frames""; ""1.1. A Dilation Viewpoint on Frames""; ""1.2. The Canonical Dual Frame""; ""1.3. Alternate Dual Frames""; ""Chapter 2. Complementary Frames and Disjointness""; ""2.1. Strong Disjointness, Disjointness and Weak Disjointness""; ""2.2. Characterizations of Equivalence and Disjointness""; ""2.3. Cuntz Algebra Generators""; ""2.4. More on Alternate Duals""; ""Chapter 3. Frame Vectors for Unitary Systems""; ""3.1. The Local Commutant and Frame Vectors""; ""3.2. Dilation Theorems for Frame Vectors""

""3.3. Equivalence Classes of Frame Vectors""""Chapter 4. Gabor Type Unitary Systems""; ""Chapter 5. Frame Wavelets, Super-wavelets and Frame Sets""; ""5.1. Frame Sets""; ""5.2. Super-wavelets""; ""5.3. A Characterization of Super-wavelets""; ""5.4. Some Frazier-Jawerth Frames""; ""5.5. MRA Super-wavelets""; ""5.6. Interpolation Theory""; ""Chapter 6. Frame Representations for Groups""; ""6.1. Basics""; ""6.2. Frame Multiplicity""; ""6.3. Parameterizations of Frame Vectors""; ""6.4. Disjoint Group Representations""; ""Chapter 7. Concluding Remarks""; ""7.1. Spectral families of frames:""

""7.2. A Joint Project with Pete Casazza""""7.3. A Matrix Completion Characterization of Frames""; ""7.4. Some Acknowledgements""; ""7.5. Density and Connectivity of Gabor Type Frames""; ""Bibliography""

Notes:

"September 2000, volume 147, number 697 (first of 4 numbers)."

Includes bibliographical references (pages 93-94).

Description based on print version record.

ISBN:

1-4704-0288-2