某类有界拟凸域双全纯不变量的极限

数学物理学报 ›› 1997, Vol. 17 ›› Issue (4): 427-431.

某类有界拟凸域双全纯不变量的极限

童武

首都师范大学数学系北京 100037

收稿日期:1996-04-02 修回日期:1996-09-07 出版日期:1997-08-26 发布日期:1997-08-26

The Limit of Biholomorphic Invariant on a Class of Pseudoconvex Domains

Tong Wu

Lept. of Math., Capital Normal University

Received:1996-04-02 Revised:1996-09-07 Online:1997-08-26 Published:1997-08-26

摘要/Abstract

摘要： E=E(m,n,k)={(z,w)∈C^n+m:|z|²+|w|^2k<1,z∈Cⁿ,w∈C^m,k>0}是C^n+m中的一类有界拟凸域.该文证明了在∂E的强拟凸点上,当m > 1时,lim_(z,w)→∂EJ_E((z,w))=((π^n+m(n+m+1)ⁿ)/((n+m)!)).m=1时,lim_(z,w)→∂EJ_E((z,w))=((πⁿ⁺¹(n+2)ⁿ⁺¹)/((n+1)!)),在∂E的弱拟凸点上,上述要限不存在.

关键词: 拟凸域, 全纯不变量, Bergman核函数

Abstract: E=E(m,n,k)={(z,w)∈C^n+m:|z|²+|w|^2k<1,z∈Cⁿ,w∈C^m,k>0} is a class of pseudoconvex domains in C^n+m. In this note is showed it, that lim_(z,w)→∂EJ_E((z,w))=π^n+m(n+m+1)ⁿ/(n+m)!,when m>1. lim_(z,w)→∂EJ_E((z,w))=πⁿ⁺¹(n+2)ⁿ⁺¹/(n+1)!, when m=1 holds on the strongly pseudoconvex points of boundary ∂E; the limit given above not exist on the weakly pseudoconvex points of boundary ∂E.

Key words: Pseudoconvex domain, Holomorphic invariant, Bergman kernel function

童武. 某类有界拟凸域双全纯不变量的极限[J]. 数学物理学报, 1997, 17(4): 427-431.

Tong Wu. The Limit of Biholomorphic Invariant on a Class of Pseudoconvex Domains[J]. Acta mathematica scientia,Series A, 1997, 17(4): 427-431.

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