**University Lecture Series**

Volume: 33;
2004;
139 pp;
Softcover

MSC: Primary 30; 42; 46; 47;

Print ISBN: 978-0-8218-3554-8

Product Code: ULECT/33

List Price: $34.00

Individual Member Price: $27.20

**Electronic ISBN: 978-1-4704-2178-6
Product Code: ULECT/33.E**

List Price: $34.00

Individual Member Price: $27.20

#### Supplemental Materials

# Interpolation and Sampling in Spaces of Analytic Functions

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*Kristian Seip*

This book contains the latest developments in a central theme of research on analysis of one complex variable. The material is based on lectures at the University of Michigan.

The exposition is about understanding the geometry of interpolating and sampling sequences in classical spaces of analytic functions. The subject can be viewed as arising from three classical topics: Nevanlinna–Pick interpolation, Carleson's interpolation theorem for \(H^\infty\), and the sampling theorem, also known as the Whittaker–Kotelnikov–Shannon theorem.

The author clarifies how certain basic properties of the space at hand are reflected in the geometry of interpolating and sampling sequences. Key words for the geometric descriptions are Carleson measures, Beurling densities, the Nyquist rate, and the Helson-Szegő condition.

Seip writes in a relaxed and fairly informal style, successfully blending informal explanations with technical details. The result is a very readable account of this complex topic.

Prerequisites are a basic knowledge of complex and functional analysis. Beyond that, readers should have some familiarity with the basics of \(H^p\) theory and BMO.

#### Table of Contents

# Table of Contents

## Interpolation and Sampling in Spaces of Analytic Functions

- Cover Cover11 free
- Title i2 free
- Copyright ii3 free
- Contents iii4 free
- Acknowledgements v6 free
- Introduction vii8 free
- Chapter 1. Carleson's interpolation theorem 114 free
- Chapter 2. Interpolating sequences and the Pick property 1528
- Chapter 3. Interpolation and sampling in Bergman spaces 4154
- Chapter 4. Interpolation in the Bloch space 6376
- Chapter 5. Interpolation, sampling, and Toeplitz operators 7992
- Chapter 6. Interpolation and sampling in Paley-Wiener spaces 95108
- Bibliography 125138
- Index 135148
- Back Cover Back Cover1153

#### Readership

Graduate students and research mathematicians interested in analysis.