Toeplitz Operators and Index Theory in Several Complex Variables (Google e-könyv)

Harald Upmeier

Springer, 1996 - 481 oldal

This book gives a comprehensive treatment of Toeplitz operators arising in multivariable complex analysis. The first part describes in detail the underlying geometric structures (strongly pseudoconvex domains, Reinhardt domains, multivariable upper half-planes, symmetric domains and generalizations) as well as the harmonic analysis of the associated Hilbert spaces of holomorphic functions (of Hardy or Bergman type). It is also of interest to mathematicians not primarily interested in operator theory. The second part of the book determines the structure of Toeplitz operators, their C*-algebras and index theory, using modern techniques such as groupoid C*-algebras, co-crossed products and operator K-theory.

Tartalomjegyzék

• 1 Multivariable Complex Analysis and Domains of Holomorphy: 1
• 11 Holomorphic Functions in Several Complex Variables: 2
• 12 Pseudoconvex Domains: 5
• 13 Tubular Domains: 11
• 14 Polycircular Domains: 30
• 15 Symmetric Domains: 43
• 16 Kcircular Domains: 67
• 17 Sbicircular Domains: 73
• 2 Harmonic Analysis on Hilbert Spaces of Holomorphic Functions: 77
• 21 Bergman Spaces Over Pseudoconvex Domains: 79
• 22 Hardy Spaces Over Strictly Pseudoconvex Domains: 86
• 23 Hardy Spaces Over Tubular Domains: 90
• 24 Bergman Spaces Over Tubular Domains: 96
• 25 Hardy Spaces Over Polycircular Domains: 108
• 26 Bergman Spaces Over Polycircular Domains: 113
• 27 The SegalBargmann Space of a Hermitian Vector Space: 115
• 28 Hardy Spaces Over Symmetric Domains: 125
• 29 Bergman Spaces Over Symmetric Domains: 141
• 210 Hardy Spaces Over Kcircular Domains: 154
• 211 Hardy Spaces Over Sbicircular Domains: 169
• 3 Multiplier C Algebras and Their Representations: 175
• 31 Hardy Multipliers Over Tubular Domains: 176
• 32 Bergman Multipliers Over Tubular Domains: 185
• 33 Hardy Multipliers Over Polycircular Domains: 188
• 34 Bergman Multipliers Over Polycircular Domains: 195
• 35 Hardy Multipliers Over Kcircular Domains: 204
• 36 Hardy Multipliers Over Symmetric Domains: 217
• 37 Hardy Multipliers Over Sbicircular Domains: 233
• 4 Toeplitz Operators and Toeplitz CAlgebras: 241
• 41 BergmanToeplitz Operators Over Bounded Domains: 242
• 42 HardyToeplitz Operators Over Strictly Pseudoconvex Domains: 250
• 43 Groupoid CAlgebras: 256
• 44 HardyToeplitz Operators Over Tubular Domains: 267
• 45 BergmanToeplitz Operators Over Tubular Domains: 278
• 46 HardyToeplitz Operators Over Polycircular Domains: 284
• 47 BergmanToeplitz Operators Over Polycircular Domains: 290
• 48 Hopf CAlgebras: 299
• 49 Actions and Coactions on CAlgebras: 310
• 410 HardyToeplitz Operators Over Kcircular Domains: 316
• 411 HardyToeplitz Operators Over Symmetric Domains: 325
• 412 BergmanToeplitz Operators Over Symmetrie Domains: 361
• 5 Index Theory for Multivariable Toeplitz Operators: 371
• 51 KTheory for Topological Spaces: 372
• 52 Index Theory for Strictly Pseudoconvex Domains: 384
• 53 KTheory for CAlgebras: 394
• 54 Index Theory for Symmetric Domains: 400
• 55 Index Theory for Tubular Domains: 432
• 56 Index Theory for Polycircular Domains: 455
• References: 462
• Index of Symbols and Notations: 471

Népszerű szakaszok

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Bibliográfiai információk

• Cím: Toeplitz Operators and Index Theory in Several Complex Variables; 81. kötet/Operator Theory: Advances and Applications; 81. kötet/Operator theory
• Szerző: Harald Upmeier
• Kiadó: Springer, 1996
• ISBN: 3764352825, 9783764352820
• Terjedelem: 481 oldal