Interpolation and Sampling in Spaces of Analytic Functions (Paperback, Illustrated Ed)

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.

General

Imprint:	American Mathematical Society
Country of origin:	United States
Series:	University Lecture Series
Release date:	March 2004
Dimensions:	254 x 178mm (L x W)
Format:	Paperback
Pages:	139
Edition:	Illustrated Ed
ISBN-13:	978-0-8218-3554-8
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > General Promotions
LSN:	0-8218-3554-8
Barcode:	9780821835548

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