ABSTRACT

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.

Features:  

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 

 

chapter 1|15 pages

Fock Space, the Heisenberg Group, Heat Flow, and Toeplitz Operators

ByLewis A. Coburn

chapter 2|47 pages

Two-Variable Weighted Shifts in Multivariable Operator Theory

ByRaúl E. Curto

chapter 4|51 pages

Operators in the Cowen-Douglas Class and Related Topics

ByGadadhar Misra

chapter 6|32 pages

Möbius Invariant Q p and Q K Spaces

ByHasi Wulan

chapter 7|19 pages

Analytical Aspects of the Drury-Arveson Space

ByQuanlei Fang, Jingbo Xia

chapter 8|36 pages

A Brief Survey of Operator Theory in H 2(𝔻2)

ByRongwei Yang

chapter 10|32 pages

Toeplitz Operators on the Bergman Space and the Berezin Transform

ByXianfeng Zhao, Dechao Zheng

chapter 11|31 pages

Towards a Dictionary for the Bargmann Transform

ByKehe Zhu