Bergman Kernel Function for Hartogs Domains Over Bounded Homogeneous Domains

被引：13

作者：

Ishi, Hideyuki ^{[1
]}

Park, Jong-Do ^{[2
,3
]}

Yamamori, Atsushi ^{[4
]}

机构：

[1] Nagoya Univ, Grad Sch Math, Chikusa Ku, Furo Cho, Nagoya, Aichi 4648602, Japan

[2] Kyung Hee Univ, Dept Math, Seoul 130701, South Korea

[3] Kyung Hee Univ, Res Inst Basic Sci, Seoul 130701, South Korea

[4] Acad Sinica 6F, Inst Math, Astron Math Bldg,1 Sec 4,Roosevelt Rd, Taipei 10617, Taiwan

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2017年 / 27卷 / 02期

基金：

新加坡国家研究基金会;

关键词：

Bergman kernel; Hartogs domains; Bounded homogeneous domains; Siegel domain; Normal j-algebra; COMPLEX ELLIPSOIDS; EXPLICIT FORMULAS; SYMMETRIC DOMAINS; SIEGEL DOMAINS; ZEROS; REPRESENTATIONS; CLASSIFICATION; CURVATURE;

D O I：

10.1007/s12220-016-9737-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain an explicit formula of the Bergman kernel for Hartogs domains over bounded homogeneous domains. In order to find a simple formula, we consider a Siegel domain biholomorphic to the bounded homogeneous domain and use its Bergman kernel obtained by Gindikin. The Bergman kernel of the Hartogs domain is expressed by two different forms and the main part of the Bergman kernel is a polynomial whose coefficients contain the Stirling number of the second kind. As an application of our formula, we investigate the Lu Qi-Keng problem for our Hartogs domains and give some important examples of Hartogs domains whose Bergman kernels are zero-free.

引用

页码：1703 / 1736

页数：34

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