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Item Details
Title: INTERPOLATION AND SAMPLING IN SPACES OF ANALYTIC FUNCTIONS
By: Kristian Seip (Editor)
Format: Paperback

List price: £61.00


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ISBN 10: 0821835548
ISBN 13: 9780821835548
Publisher: AMERICAN MATHEMATICAL SOCIETY
Pub. date: 15 March, 2004
Series: University Lecture Series No. 33
Pages: 139
Description: Contains the developments in a central theme of research on analysis of one complex variable. This book includes material that is based on lectures at the University of Michigan. It clarifies how certain basic properties of the space at hand are reflected in the geometry of interpolating and sampling sequences.
Synopsis: 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.
Publication: US
Imprint: American Mathematical Society
Returns: Returnable
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