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Synopsis
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.
Booknews
A comprehensive treatment of Toepliz operators in multivariable complex analysis describing the detail underlying geometric structures, and harmonic analysis of the associated Hilbert spaces of holomorphic functions. Some of the topics covered within this context include pseudoconvex domains, Reinhardt domains, symmetric domains and generalizations, a determination of the structure of Toeplitz operators, their C*-algebras and index theory, and modern groupoid C* algebra techniques, co-crossed products and operator K-theory. Annotation c. Book News, Inc., Portland, OR (booknews.com)