Theory of Complex Homogeneous Bounded Domains
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.
This book is suitable for graduate students, and researchers in mathematics.
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acting simply transitively acts transitively Aff D(V Aff VN affine automorphism group affine isomorphism Aut D(V automorphism group Aut Bergman kernel Bergman kernel function Bergman mapping Bergman metric canonical form Cartan Cauchy-Szego kernel function characteristic boundary compact subgroup complex matrix convex cone D(VN defined Definition Denote diag direct computation direct sum decomposition effective J Lie element exists give group Aff Hence Hermitian Hermitian matrix holomorphic automorphism group holomorphic function holomorphic isomorphism homogeneous bounded domain homogeneous Siegel domain implies indecomposable invariant isotropy subgroup Lemma Lie subalgebra linear transformation manifold matrix representation non-semisimple normal J Lie normal matrix set normal Siegel domain orthonormal basis Poisson kernel Proof real analytic real matrix real normal matrix satisfies condition satisfies the condition semisimple Lie algebra set of type Siegel domain D(VN,F square cone symmetric matrix transformation group unit connected component unitary matrix vector field