Mathematical Surveys and Monographs 2004; 318 pp; hardcover Volume: 100 ISBN10: 0821808109 ISBN13: 9780821808108 List Price: US$92 Member Price: US$73.60 Order Code: SURV/100
 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 selfcontained introduction to a broad range of topics, including recent advances on interpolation and sampling, contractive zerodivisors, 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
 Zerosets
 Contractive zerodivisors
 Sampling and interpolation
 Proofs of sampling and interpolation theorems
 Invariant subspaces
 Structure of invariant subspaces
 References
 Index
