Quadrature Domains in \({{\mathbb C}}^n\)

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• 作者：Pranav Haridas ; Kaushal Verma
• 关键词：Quadrature domains ; Condition R ; Bergman kernel ; 32A36 ; 32A25
• 刊名：Computational Methods and Function Theory
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：15
• 期：1
• 页码：125-141
• 全文大小：248 KB
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• 刊物主题：Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable;
• 出版者：Springer Berlin Heidelberg
• ISSN：2195-3724

文摘

We prove two density theorems for quadrature domains in \(\mathbb {C}^n\) , \(n \ge 2\) . It is shown that quadrature domains are dense in the class of all product domains of the form \(D \times \Omega \) , where \(D \subset \mathbb {C}^{n-1}\) is a smoothly bounded domain satisfying Bell’s Condition R and \(\Omega \subset \mathbb {C}\) is a smoothly bounded domain and also in the class of all smoothly bounded complete Hartogs domains in \(\mathbb {C}^2\) .