**Contemporary Mathematics**

Volume: 679;
2016;
217 pp;
Softcover

MSC: Primary 11; 30; 35; 47;

**Print ISBN: 978-1-4704-2305-6
Product Code: CONM/679**

List Price: $108.00

AMS Member Price: $86.40

MAA Member Price: $97.20

**Electronic ISBN: 978-1-4704-3627-8
Product Code: CONM/679.E**

List Price: $108.00

AMS Member Price: $86.40

MAA Member Price: $97.20

# Recent Progress on Operator Theory and Approximation in Spaces of Analytic Functions

Share this page *Edited by *
*Catherine Bénéteau; Alberto A. Condori; Constanze Liaw; William T. Ross; Alan A. Sola*

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.

#### Readership

Graduate students and research mathematicians interested in operator theory and complex analysis.

# Table of Contents

## Recent Progress on Operator Theory and Approximation in Spaces of Analytic Functions

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Properties of vector-valued submodules on the bidisk 112
- Composition operators on the Hardy–Hilbert space 𝐻² and model spaces 𝐾_{Θ} 1324
- 1. Introduction 1324
- 2. The Hardy–Hilbert space 𝐻² 1425
- 3. The Littlewood subordination principle 1829
- 4. A Schröder-type equation 2435
- 5. The group (\D,*) 2940
- 6. An equivalence relation on \overline{\D} 3445
- 7. Minimal Blaschke products 3849
- 8. Composition of singular inner functions 4051
- 9. Model spaces 4960
- References 5364

- A survey of some recent results on truncated Toeplitz operators 5970
- Approximating \overline{𝑧} in the Bergman Space 7990
- Real complex functions 91102
- Thin Interpolating Sequences 129140
- 1. The beginning of interpolation in Hardy spaces 129140
- 2. Best bounds and best functions 130141
- 3. The maximal ideal space 135146
- 4. Thin sequences, interpolation and uniform algebras 137148
- 5. Extending the definition of thin to 𝐻^{𝑝} spaces 138149
- 6. Maximal ideal space and operator theory 139150
- 7. Asymptotically orthonormal sequences 140151
- 8. Carleson measures and thin sequences 141152
- 9. Future Directions: Model Spaces 143154
- References 144155

- Kernels of Toeplitz operators 147158
- 1. Introduction 147158
- 2. Basic definitions 153164
- 3. Invertibility and left-invertibility of Toeplitz operators 156167
- 4. Injectivity of Toeplitz operators and rigid functions 158169
- 5. Kernels of Toeplitz operators and extremal functions 159170
- 6. Bourgain factorization 162173
- 7. More on the case 𝑝≠2 163174
- 8. Triviality of Toeplitz kernels and applications 167178
- References 175186

- Some open questions in analysis for Dirichlet series 179190
- 1. Introduction 179190
- 2. Basic properties of the spaces \Hp and 𝐻^{𝑝}(\T^{∞}) 181192
- 3. Operator theory and harmonic analysis 182193
- 4. Moments of sums of random multiplicative functions 183194
- 5. Estimates for GCD sums and the Riemann zeta function 184195
- 6. Random Dirichlet series 187198
- References 188199

- Some problems on optimal approximants 193204
- 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 207218
- Back Cover Back Cover1230