Toeplitz operators and index theory in several complex variables

the long version

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 Hibert 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.