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AuthorUpmeier, Harald. author
TitleToeplitz Operators and Index Theory in Several Complex Variables [electronic resource] / by Harald Upmeier
ImprintBasel : Birkhรคuser Basel, 1996
Connect tohttp://dx.doi.org/10.1007/978-3-0348-9246-9
Descript XI, 483 p. online resource

SUMMARY

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


CONTENT

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


Mathematics Mathematical analysis Analysis (Mathematics) Functions of complex variables Geometry Mathematics Geometry Analysis Functions of a Complex Variable



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