Holomorphic Spaces

by Edited by Sheldon Axler , John E. McCarthy , Donald Sarason

• ISBN13: 9780521101035
• ISBN10: 0521101034
• Edition: 1st
• Format: Paperback
• Copyright: 2009-02-05
• Publisher: Cambridge University Press

Summary

Spaces of holomorphic functions have been a prominent theme in analysis since early in the twentieth century. Of interest to complex analysts, functional analysts, operator theorists, and systems theorists, their study is now flourishing. This volume, an outgrowth of a 1995 program at the Mathematical Sciences Research Institute, contains expository articles by program participants describing the present state of the art. Here researchers and graduate students will encounter Hardy spaces, Bergman spaces, Dirichlet spaces, Hankel and Toeplitz operators, and a sampling of the role these objects play in modern analysis.

Table of Contents

Preface

Holomorphic spaces: a brief and selective survey

Recent progress in the function theory of the Bergman space

Harmonic Bergman spaces

An excursion into the theory of Hankel operators

Hankel-type operators, Bourgain algebras and uniform algebras

Tight uniform algebras

Higher-order Hankel forms and commutators

Function theory and operator theory on the Dirichlet space

Some open problems in the theory of subnormal operators

Elements of spectral theory in terms of the free function model part I: basic constructions

Liftings of kernels shift-invariant in scattering systems

Some function-theoretic issues in feedback stabilisation

The abstract interpolation problem

A basic interpolation problem

Reproducing kernel Pontryagin spaces

Commuting operators and function theory on a Riemann surface

Table of Contents provided by Publisher. All Rights Reserved.