Theory of Complex Homogeneous Bounded Domains

Yichao Xu (auth.)1402021321, 9781402021329, 7030123352, 9787030123350, 140202133X, 9781402021336

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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Table of contents :
Siegel Domains….Pages 1-46
Homogeneous Siegel Domains….Pages 47-100
Normal Siegel Domains….Pages 101-150
Other Realizations….Pages 151-180
Automorphism Group….Pages 181-236
Classification of Square Domains….Pages 237-290
Symmetric Bounded Domains….Pages 291-328
Szegö Kernel and Poisson Kernel….Pages 329-360
Homogeneous Bounded Domains….Pages 361-410