On the Zeros of the Slice Bergman Kernels for the Upper Half Space and the Unit Ball on Quaternions and Clifford Algebras

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• 作者：Jong-Do Park
• 关键词：Bergman kernel ; Quaternionic analysis ; Slice regular functions ; Clifford algebra ; Slice monogenic functions ; Lu Qi ; Keng domains
• 刊名：Complex Analysis and Operator Theory
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：11
• 期：2
• 页码：329-344
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Operator Theory; Analysis;
• 出版者：Springer International Publishing
• ISSN：1661-8262
• 卷排序：11

文摘

In the complex analysis, it is a well-known problem to determine whether the Bergman kernel for a given domain has zeros or not. The Bergman kernels for the upper half plane and the unit ballare zero-free. We prove that this phenomenon also holds in the setting of quaternions and the real Clifford algebras.