Interpolation and Sampling in Spaces of Analytic Functions

Kristian Seip

ISBN 10: 0821835548 / ISBN 13: 9780821835548

Published by American Mathematical Society, US, 2004

About this Item

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-Szego 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.

Seller Inventory # LU-9780821835548

Bibliographic Details

• Title: Interpolation and Sampling in Spaces of Analytic Functions
• Publisher: American Mathematical Society, US
• Publication Date: 2004
• Language: English
• ISBN 10: 0821835548
• ISBN 13: 9780821835548
• Binding: Paperback
• Condition: New

About this title

Synopsis

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. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)