Frames and harmonic analysis : AMS special sessions on frames, wavelets, and Gabor systems and frames, harmonic analysis, and operator theory, April 16-17, 2016, North Dakota State University, Fargo, North Dakota / Yeonhyang Kim [and three others], editors.

Format:

Book

Contributor:

Kim, Yeonhyang, 1972- editor.

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 706

Contemporary mathematics, 706 0271-4132

Language:

English

Subjects (All):

Frames (Vector analysis).

Harmonic analysis.

Wavelets (Mathematics).

Gabor transforms.

Physical Description:

1 online resource (xii, 343 pages).

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2018]

Summary:

This volume contains the proceedings of the AMS Special Sessions on Frames, Wavelets and Gabor Systems and Frames, Harmonic Analysis, and Operator Theory, held from April 16-17, 2016, at North Dakota State University in Fargo, North Dakota. The papers appearing in this volume cover frame theory and applications in three specific contexts: frame constructions and applications, Fourier and harmonic analysis, and wavelet theory.

Contents:

Cover

Title page

Contents

Preface

Participants of the AMS Special Session "Frames, Wavelets and Gabor Systems"

Participants of the AMS Special Session "Frames, Harmonic Analysis, and Operator Theory"

Constructions of biangular tight frames and their relationships with equiangular tight frames

1. Introduction

2. Preliminaries

3. A continuum of BTFs in ℝ³

4. Harmonic BTFs

5. Steiner BTFs

6. Plücker ETFs

Acknowledgment

References

Phase retrieval by hyperplanes

3. Phase retrieval by hyperplanes

4. An example in \RR⁴

Tight and full spark Chebyshev frames with real entries and worst-case coherence analysis

2. Real Vandermonde-like matrices

3. Frames seeded from DFT matrices

Fusion frames and distributed sparsity

2. General tools and models

3. An extension of traditional compressed sensing

4. Application to dense spectrum estimation

5. Conclusion

The Kadison-Singer problem

2. From Kadison-Singer problem to Weaver's conjecture

3. Proof of Weaver's conjecture

4. Applications of Weaver's conjecture

Acknowledgments

Spectral properties of an operator polynomial with coefficients in a Banach algebra

2. Banach modules and memory decay

3. The method of similar operators and a special case of the main result

4. Proof of the main result

5. Various classes of operators with memory decay

6. Examples

The Kaczmarz algorithm, row action methods, and statistical learning algorithms

2. Connection with projection methods and row action methods

3. Convergence rate of Kaczmarz algorithm under noise

4. Connection with statistical learning methods.

References

Lipschitz properties for deep convolutional networks

2. Scattering network

3. Filter aggregation

4. Examples of estimating the Lipschitz constant

Invertibility of graph translation and support of Laplacian Fiedler vectors

2. Translation operator on graphs

3. Support of Laplacian Fiedler vectors on graphs

Weighted convolution inequalities and Beurling density

2. Weighted convolution inequalities and Beurling densities of the measure ⁻¹

3. Best constants in weighted convolution inequalities

4. Exponential weights

Acknowledgements

-Riesz bases in quasi shift invariant spaces

3. Problem 1 ( =2)

4. Problem 2

5. Remarks and open problems

On spectral sets of integers

2. One prime power

3. Szabó's examples

4. Some general constructions

5. Appendix

Spectral fractal measures associated to IFS's consisting of three contraction mappings

1. Introduction: Hutchinson measures and determining when they are spectral

2. Spectral Hutchinson-3 measures: a necessary condition on for the resulting measure to be spectral

3. Well-spacedness about the origin and the canonical spectrum

4. Well-spacedness about the origin and an alternative spectrum

5. Which Hutchinson-3 measures are spectral?

A matrix characterization of boundary representations of positive matrices in the Hardy space

2. Lebesgue measure: kernels in ²( ) with equal norms

3. Diagonal coefficient matrices

4. Absolutely continuous measures

5. Preservation of norms of subspaces of ²( )

References.

Gibbs effects using Daubechies and Coiflet tight framelet systems

2. Daubechies and Coiflets tight framelets for two generators

3. The Gibbs phenomenon in Daubechies and Coiflets tight framelet expansions

4. Conclusion

Conditions on shape preserving of stationary polynomial reproducing subdivision schemes

2. Conditions for shape preservaton

-Markov measures, transfer operators, wavelets and multiresolutions

2. General theory

3. Solenoid probability spaces

4. Examples and applications: Transfer operators and Markov moves

Back Cover.

Notes:

Description based on print version record.

ISBN:

1-4704-4723-1