Based on a series of six lectures given by the author at the University of Michigan, this book is intended as an introduction to the topic of interpolation and sampling in analytic function spaces. The three major topics covered are Nevanlinna-Pick interpolation, Carleson's interpolation theorem, and the Whittaker-Kotelnikov-Shannon theorem. The style, being more discursive than the almost fetishistic terseness found in many textbooks, reflects the lecture hall origin of the book, as do the delightfully minimal background knowledge requirements.
CONTENTS
Acknowledgements
Introduction
Chapter 1. Carleson's interpolation theorem
Chapter 2. Interpolating sequences and the Pick property
Chapter 3. Interpolation and sampling in Bergman spaces
Chapter 4. Interpolation in the Bloch space
Chapter 5. Interpolation, sampling, and Toeplitz operators
Chapter 6. Interpolation and sampling in Paley-Wiener spaces
Bibliography
Index
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