Interpolation and Sampling in Spaces of Analytic Functions (University Lecture Series) by Kristian Seip (PDF)

Description

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-Szegö 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.

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