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Toeplitz Operators and Index Theory in Several Complex Variables

  • Book
  • © 1996

Overview

Authors:
  1. Harald Upmeier

    1. Department of Mathematics, University of Marburg, Marburg, Germany

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Part of the book series: Operator Theory: Advances and Applications (OT, volume 81)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xi
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  2. Multi-variable Complex Analysis and Domains of Holomorphy

    • Harald Upmeier
    Pages 1-76

  3. Harmonic Analysis on Hilert Spaces of Holomorphic Functions

    • Harald Upmeier
    Pages 77-174

  4. Multiplier C* -Algebras and Their Representations

    • Harald Upmeier
    Pages 175-240

  5. Toeplitz Operators and Toeplitz C*-Algebras

    • Harald Upmeier
    Pages 241-370

  6. Index Theory for Multivariable Toeplitz Operators

    • Harald Upmeier
    Pages 371-461

  7. Back Matter

    Pages 462-483
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, University of Marburg, Marburg, Germany

    Harald Upmeier

Bibliographic Information

  • Book Title: Toeplitz Operators and Index Theory in Several Complex Variables

  • Authors: Harald Upmeier

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-9246-9

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag 1996

  • Hardcover ISBN: 978-3-7643-5282-0Published: 26 January 1995

  • Softcover ISBN: 978-3-0348-9960-4Published: 27 September 2011

  • eBook ISBN: 978-3-0348-9246-9Published: 06 December 2012

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: XI, 483

  • Topics: Geometry, Analysis, Functions of a Complex Variable

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