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Bergman Spaces
Peter Duren, University of Michigan, Ann Arbor, MI, and Alexander Schuster, San Francisco State University, CA
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Mathematical Surveys and Monographs
2004; 318 pp; hardcover
Volume: 100
ISBN-10: 0-8218-0810-9
ISBN-13: 978-0-8218-0810-8
List Price: US$87
Member Price: US$69.60
Order Code: SURV/100
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Over the last ten years, the theory of Bergman spaces has undergone a remarkable metamorphosis. In a series of major advances, central problems once considered intractable were solved, and a rich theory emerged. Although progress continues, the time seems ripe for a full and unified account of the subject, weaving the old and new results together. This thorough exposition provides just that.

The subject of Bergman spaces is a masterful blend of complex function theory with functional analysis and operator theory. It has much in common with Hardy spaces, but involves new elements such as hyperbolic geometry, reproducing kernels, and biharmonic Green functions.

In this book, the authors develop background material and provide a self-contained introduction to a broad range of topics, including recent advances on interpolation and sampling, contractive zero-divisors, and invariant subspaces. The book is accessible to researchers and advanced graduate students who have studied basic complex function theory, measure theory, and functional analysis.

Readership

Advanced graduate students and research mathematicians interested in complex function theory and operator theory.

Table of Contents

  • Overview
  • The Bergman kernel function
  • Linear space properties
  • Analytic properties
  • Zero-sets
  • Contractive zero-divisors
  • Sampling and interpolation
  • Proofs of sampling and interpolation theorems
  • Invariant subspaces
  • Structure of invariant subspaces
  • References
  • Index
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