Handbook of Analytic Operator Theory thoroughly covers the subject of holomorphic function spaces and operators acting on them. The spaces covered include Bergman spaces, Hardy spaces, Fock spaces and the Drury-Averson space. Operators discussed in the book include Toeplitz operators, Hankel operators, composition operators, and Cowen-Douglas class operators.
The volume consists of eleven articles in the general area of analytic function spaces and operators on them. Each contributor focuses on one particular topic, for example, operator theory on the Drury-Aversson space, and presents the material in the form of a survey paper which contains all the major results in the area and includes all relevant references.
The overalp between this volume and existing books in the area is minimal. The material on two-variable weighted shifts by Curto, the Drury-Averson space by Fang and Xia, the Cowen-Douglas class by Misra, and operator theory on the bi-disk by Yang has never appeared in book form before.
The editor of the handbook is a widely known and published researcher on this topic
The handbook's contributors are a who's=who of top researchers in the area
The first contributed volume on these diverse topics
Table of Contents
The Drury Arveson space and related operator theory. The Dirichlet space and related operator theory. Fock spaces and related operator theory. The Hardy space of the bi-disk and related operator theory. Toeplitz operators on the Bergman space. Hankel operators on the Bergman space. Bounded symmetric domains and Toeplitz operators. Composition operators. Operators in Cowen-Douglas classes. Invariant subspaces of the Bergman space. Mobius invariant Qp and Qk spaces. Spaces of Dirichlet series and related operator theory. The corona problem and related function/operator theory
Kehe Zhu is professor of mathematics at the State University of New York at Albany. His research areas are complex analysis, functional analysis, and operator theory. He has published over 110 papers in leading research journals in mathematics. He has also published several books including Theory of Bergman Spaces, Spaces of Holomorphic Functions in the Unit Ball, Analysis on Fock Spaces, Mobius Invariant Qk Spaces, Operator Theory in Function Spaces, and An Introduction to Operator Algebras (CRC Press).