Bergman Spaces (Mathematical Surveys and Monographs)
by Peter L. Duren, Alexander Schuster
Category: Mathematics

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.