The Bergman Kernels on WⅢ
Author(s): LU Ke-ping, ZHAO Xiao-xia
Pages: 24-29
Year: 2004 Issue: 1
Journal: CHINESE QUARTERLY JOURNAL OF MATHEMATICS
Keyword: Bergman kernel function; holomorphic automorphism group; complete orthonormal system;
Abstract: In this paper,we compute the Bergman kernel function on WⅢ.WⅢ = { W2 ∈ C,(W1,Z) ∈ YⅢ(q) | |W2|2p ＜ (1 - X)2det (I + ZZ) }.Where YⅢ = { (W1,Z) ||W1 |2k ＜ det (I+ZZ),Z ∈ RⅢ },X = X(W1,Z) = |W1|2det (I+ZZ)-1/k,and RⅢ(q) denote the Cartan domain of the third class.Because domain WⅢis neither homogeneous domain nor Reinhardt domain,we will use a new way to solve this problem.First,we give a holomorphic automorphism group,such that for any Z0,there exists an element of this group,which maps (W,Z0) into (W*,0).Second,introduce the concept of semi-Reinhardt and discuss the complete orthonormal system of this domain.
Pages: 24-29
Year: 2004 Issue: 1
Journal: CHINESE QUARTERLY JOURNAL OF MATHEMATICS
Keyword: Bergman kernel function; holomorphic automorphism group; complete orthonormal system;
Abstract: In this paper,we compute the Bergman kernel function on WⅢ.WⅢ = { W2 ∈ C,(W1,Z) ∈ YⅢ(q) | |W2|2p ＜ (1 - X)2det (I + ZZ) }.Where YⅢ = { (W1,Z) ||W1 |2k ＜ det (I+ZZ),Z ∈ RⅢ },X = X(W1,Z) = |W1|2det (I+ZZ)-1/k,and RⅢ(q) denote the Cartan domain of the third class.Because domain WⅢis neither homogeneous domain nor Reinhardt domain,we will use a new way to solve this problem.First,we give a holomorphic automorphism group,such that for any Z0,there exists an element of this group,which maps (W,Z0) into (W*,0).Second,introduce the concept of semi-Reinhardt and discuss the complete orthonormal system of this domain.
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