Theory of Complex Homogeneous Bounded Domains / by Yichao Xu.

Springer eBooks

1. Siegel Domains and sub chapters -- 2. Homogeneous Siegel Domains and sub chapters -- 3. Normal Siegel Domains and sub chapters -- 4. Other Realizations and sub chapters -- 5. Automorphism Group and sub chapters -- 6. Classification of Square Domains and sub chapters -- 7. Symmetric Bounded Domains and sub chapters -- 8. Szegö Kernel and Poisson Kernel and sub chapters -- 9. Homogeneous Bounded Domains and sub chapters -- References. Index.

Theory of Complex Homogeneous Bounded Domains studies the classification and function theory of complex homogeneous bounded domains systematically for the first time. In the book, the Siegel domains are discussed in detail. Proofs are given for 1: every homogeneous bounded domain is holomorphically isomorphic to a homogeneous Siegel domain, and 2: every homogeneous Siegel domain is affine isomorphic to a normal Siegel domain. Using the normal Siegel domains to realize the homogeneous bounded domains, we can obtain more property of the geometry and the function theory on homogeneous bounded domains.

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