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4. 1 BergmanToeplitz Operators Over Bounded Domains 242 4. 2 HardyToeplitz Operators Over Strictly Domains Pseudoconvex 250 Groupoid C* Algebras 4. 3 256 4. 4 HardyToeplitz Operators Over Tubular Domains 267 4. 5 BergmanToeplitz Operators Over Tubular Domains 278 4. 6 HardyToeplitz Operators Over Polycircular Domains 284 4. 7 BergmanToeplitz Operators Over Polycircular Domains 290 4. 8 Hopf C* Algebras 299 4. 9 Actions and Coactions on C* Algebras 310 4. 10 HardyToeplitz Operators Over Kcircular Domains 316 4. 11 HardyToeplitz Operators Over Symmetric Domains 325 4. 12 BergmanToeplitz Operators Over Symmetric Domains 361 5. Index Theory for Multivariable Toeplitz Operators 5. 0 Introduction 371 5. 1 KTheory for Topological Spaces 372 5. 2 Index Theory for Strictly Pseudoconvex Domains 384 5. 3 C*Algebras KTheory 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 Itorus) and the closely related WienerHopf operators (on the halfline) 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.
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