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.
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.
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.
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