Conformal Models and Fingerprints of Pseudo-lemniscates

详细信息    查看全文

• 作者：Trevor Richards ; Malik Younsi
• 关键词：Meromorphic functions ; Conformal welding ; Conformal models ; Pseudo ; lemniscates ; Fingerprints
• 刊名：Constructive Approximation
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：45
• 期：1
• 页码：129-141
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Numerical Analysis; Analysis;
• 出版者：Springer US
• ISSN：1432-0940
• 卷排序：45

文摘

We prove that every meromorphic function on the closure of an analytic Jordan domain that is sufficiently well-behaved on the boundary is conformally equivalent to a rational map whose degree is smallest possible. We also show that the minimality of the degree fails in general without the boundary assumptions. As an application, we generalize a theorem of Ebenfelt, Khavinson, and Shapiro by characterizing fingerprints of polynomial pseudo-lemniscates.