| 第三类华罗庚域的Bergman核函数 |
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| 引用本文： | 殷慰萍,赵晓霞.第三类华罗庚域的Bergman核函数[J].数学年刊A辑(中文版),2003(1). |
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| 作者姓名： | 殷慰萍 赵晓霞 |
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| 作者单位： | 首都师范大学数学系，首都师范大学数学系 北京 100037，北京 100037 |
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| 基金项目： | 国家自然科学基金(No.10171068)，北京市自然科学基金(No.1012004)资助的项目 |
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| 摘 要： | 本文主要是计算第三类华罗庚域的Bergman核函数的显式表达式.由于华罗庚域既不是齐性域又不是Reinhardt域,故以往求Bergman核函数的方法都行不通.本文用新的方法进行计算.关键之处有两点:一是给出第三类华罗庚域的全纯自同构群,群中每一元素将形为(W,Z0)的内点映为点(W*,0);二是引进了semi—Reinhardt的概念并求出了其完备标准正交函数系.
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| 关 键 词： | 华罗庚域 Bergman核函数 全纯自同构群 完备标准正交函数系 |
THE BERGMAN KERNELS ON HUA DOMAIN OF THE THIRD TYPE |
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| YIN Weiping ZHAO Xiaoxia.THE BERGMAN KERNELS ON HUA DOMAIN OF THE THIRD TYPE[J].Chinese Annals of Mathematics,2003(1). |
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| Authors: | YIN Weiping ZHAO Xiaoxia |
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| Institution: | YIN Weiping ZHAO Xiaoxia Department of Mathematics,Capital Normal University,Beijing 100037,China. |
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| Abstract: | In this paper the Bergman kernels on Hua domain of the third type (HEm) are given in explicit formulas. Hua domain is both non-Reinhardt and non-homogeneous, therefore the authors use a new method to compute its Bergman kernel. The new method has two key steps: one is to get the automorphism group of HEm, and the another one is to introduce the concept of semi-Reinhardt domain and get its complete orthonornal system. |
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| Keywords: | Hua domain Bergman kernels function Automorphism group Complete orthonornal system |
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