Recent progress on operator theory and approximation in spaces of analytic functions : Conference on Completeness Problems, Carleson Measures, and Spaces of Analytic Functions, June 29-July 3, 2015, Institut Mittag-Leffler, Djursholm, Sweden / Catherine Bénéteau [and four others], editors.

Format:

Book

Contributor:

Bénéteau, Catherine, editor.

Series:

Contemporary mathematics (American Mathematical Society) ; 679.

Contemporary Mathematics, 1098-3627 ; 679

Language:

English

Subjects (All):

Operator theory--Congresses.

Operator theory.

Analytic spaces--Congresses.

Analytic spaces.

Analytic functions--Congresses.

Analytic functions.

Physical Description:

1 online resource (230 pages) : illustrations.

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2016.

Summary:

This volume contains the Proceedings of the Conference on Completeness Problems, Carleson Measures, and Spaces of Analytic Functions, held from June 29-July 3, 2015, at the Institut Mittag-Leffler, Djursholm, Sweden. The conference brought together experienced researchers and promising young mathematicians from many countries to discuss recent progress made in function theory, model spaces, completeness problems, and Carleson measures. This volume contains articles covering cutting-edge research questions, as well as longer survey papers and a report on the problem session that contains a collection of attractive open problems in complex and harmonic analysis.

Contents:

Cover

Title page

Contents

Preface

Properties of vector-valued submodules on the bidisk

1. Introduction

2. Products of One-Variable Inner Functions

3. Relationship Between Degree of Θ and Rank of [ _{ ⱼ}, *_{ ⱼ}]

4. Some Examples

References

Composition operators on the Hardy-Hilbert space ² and model spaces _{Θ}

2. The Hardy-Hilbert space ²

3. The Littlewood subordination principle

4. A Schröder-type equation

5. The group (\D,*)

6. An equivalence relation on \overline{\D}

7. Minimal Blaschke products

8. Composition of singular inner functions

9. Model spaces

A survey of some recent results on truncated Toeplitz operators

2. Preliminaries

3. Carleson measures

4. Truncated Toeplitz operators

5. Compact operators

6. Compact TTOs and embedding measures

7. TTOs in other ideals

8. Invertibility and Fredholmness

Acknowledgements

Approximating \overline{ } in the Bergman Space

2. Results

3. Examples

4. Bergman Analytic Content

5. Concluding Remarks

Acknowledgment

Real complex functions

2. Function spaces

3. Elementary observations

4. Unilateral Products of Cayley Inner Functions

5. Herglotz -integral representations

6. Bilateral products

7. Real complex functions in operator theory

Thin Interpolating Sequences

1. The beginning of interpolation in Hardy spaces

2. Best bounds and best functions

3. The maximal ideal space

4. Thin sequences, interpolation and uniform algebras

5. Extending the definition of thin to ^{ } spaces

6. Maximal ideal space and operator theory

7. Asymptotically orthonormal sequences

8. Carleson measures and thin sequences.

9. Future Directions: Model Spaces

Kernels of Toeplitz operators

2. Basic definitions

3. Invertibility and left-invertibility of Toeplitz operators

4. Injectivity of Toeplitz operators and rigid functions

5. Kernels of Toeplitz operators and extremal functions

6. Bourgain factorization

7. More on the case ≠2

8. Triviality of Toeplitz kernels and applications

Some open questions in analysis for Dirichlet series

2. Basic properties of the spaces \Hp and ^{ }(\T^{∞})

3. Operator theory and harmonic analysis

4. Moments of sums of random multiplicative functions

5. Estimates for GCD sums and the Riemann zeta function

6. Random Dirichlet series

Some problems on optimal approximants

2. Polynomial proofs of cyclicity theorems

3. Examples and the role of the logarithmic potential

4. Higher dimensional phenomena

Some open problems in complex and harmonic analysis: Report on problem session held during the conference Completeness problems, Carleson measures, and spaces of analytic functions

1. Overview

2. Approximation in de Branges-Rovnyak spaces

3. Inverse spectral problems, completeness of exponentials, and meromorphic inner functions

4. Quadratic differential operators and Weyl-quantization of quadratic forms

Back Cover.

Notes:

Includes bibliographical references at the end of each chapters.

Description based on print version record.

ISBN:

1-4704-3627-2