Toeplitz Operators and Index Theory in Several Complex Variables / Edition 1

by Harald Upmeier

Overview

4. 1 Bergman-Toeplitz Operators Over Bounded Domains 242 4. 2 Hardy-Toeplitz Operators Over Strictly Domains Pseudoconvex 250 Groupoid C* -Algebras 4. 3 256 4. 4 Hardy-Toeplitz Operators Over Tubular Domains 267 4. 5 Bergman-Toeplitz Operators Over Tubular Domains 278 4. 6 Hardy-Toeplitz Operators Over Polycircular Domains 284 4. 7 Bergman-Toeplitz Operators Over Polycircular Domains 290 4. 8 Hopf C* -Algebras 299 4. 9 Actions and Coactions on C* -Algebras 310 4. 10 Hardy-Toeplitz Operators Over K-circular Domains 316 4. 11 Hardy-Toeplitz Operators Over Symmetric Domains 325 4. 12 Bergman-Toeplitz Operators Over Symmetric Domains 361 5. Index Theory for Multivariable Toeplitz Operators 5. 0 Introduction 371 5. 1 K-Theory for Topological Spaces 372 5. 2 Index Theory for Strictly Pseudoconvex Domains 384 5. 3 C*-Algebras K-Theory for 394 5. 4 Index Theory for Symmetric Domains 400 5. 5 Index Theory for Tubular Domains 432 5. 6 Index Theory for Polycircular Domains 455 References 462 Index of Symbols and Notations 471 In trod uction Toeplitz operators on the classical Hardy space (on the I-torus) and the closely related Wiener-Hopf operators (on the half-line) form a central part of operator theory, with many applications e. g. , to function theory on the unit disk and to the theory of integral equations.

Product Details

ISBN-13:	9783764352820
Publisher:	Birkhäuser Basel
Publication date:	01/26/1995
Series:	Operator Theory: Advances and Applications , #81
Edition description:	1996
Pages:	483
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

1. Multi-variable Complex Analysis and Domains of Holomorphy.- 1.0 Introduction.- 1.1 Holomorphic Functions in Several Complex Variables.- 1.2 Pseudoconvex Domains.- 1.3 Tubular Domains.- 1.4 Polycircular Domains.- 1.5 Symmetric Domains.- 1.6 K-circular Domains.- 1.7 S-bicircular Domains.- 2. Harmonic Analysis on Hilbert Spaces of Holomorphic Functions.- 2.0 Introduction.- 2.1 Bergman Spaces Over Pseudoconvex Domains.- 2.2 Hardy Spaces Over Strictly Pseudoconvex Domains.- 2.3 Hardy Spaces Over Tubular Domains.- 2.4 Bergman Spaces Over Tubular Domains.- 2.5 Hardy Spaces Over Polycircular Domains.- 2.6 Bergman Spaces Over Polycircular Domains.- 2.7 The Segal-Bargmann Space of a Hermitian Vector Space.- 2.8 Hardy Spaces Over Symmetric Domains.- 2.9 Bergman Spaces Over Symmetric Domains.- 2.10 Hardy Spaces Over K-circular Domains.- 2.11 Hardy Spaces Over S-bicircular Domains.- 3. Multiplier C*-Algebras and Their Representations.- 3.0 Introduction.- 3.1 Hardy Multipliers Over Tubular Domains.- 3.2 Bergman Multipliers Over Tubular Domains.- 3.3 Hardy Multipliers Over Polycircular Domains.- 3.4 Bergman Multipliers Over Polycircular Domains.- 3.5 Hardy Multipliers Over K-circular Domains.- 3.6 Hardy Multipliers Over Symmetric Domains.- 3.7 Hardy Multipliers Over S-bicircular Domains.- 4. Toeplitz Operators and Toeplitz C*-Algebras.- 4.0 Introduction.- 4.1 Bergman-Toeplitz Operators Over Bounded Domains.- 4.2 Hardy-Toeplitz Operators Over Strictly Pseudoconvex Domains.- 4.3 Groupoid C*-Algebras.- 4.4 Hardy-Toeplitz Operators Over Tubular Domains.- 4.5 Bergman-Toeplitz Operators Over Tubular Domains.- 4.6 Hardy-Toeplitz Operators Over Polycircular Domains.- 4.7 Bergman-Toeplitz Operators Over Polycircular Domains.- 4.8 Hopf C*-Algebras.- 4.9 Actions and Coactions on C*-Algebras.-4.10 Hardy-Toeplitz Operators Over K-circular Domains.- 4.11 Hardy-Toeplitz Operators Over Symmetric Domains.- 4.12 Bergman-Toeplitz Operators Over Symmetric Domains.- 5. Index Theory for Multivariable Toeplitz Operators.- 5.0 Introduction.- 5 .1 K-Theory for Topological Spaces.- 5.2 Index Theory for Strictly Pseudoconvex Domains.- 5.3 K-Theory for C*-Algebras.- 5.4 Index Theory for Symmetric Domains.- 5.5 Index Theory for Tubular Domains.- 5.6 Index Theory for Polycircular Domains.- References.- Index of Symbols and Notations.

Editorial Reviews

A comprehensive treatment of Toepliz operators in multivariable complex analysis describing the detail underlying geometric structures, and harmonic analysis of the associated Hilbert spaces of holomorphic functions. Some of the topics covered within this context include pseudoconvex domains, Reinhardt domains, symmetric domains and generalizations, a determination of the structure of Toeplitz operators, their C*-algebras and index theory, and modern groupoid C* algebra techniques, co-crossed products and operator K-theory. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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