Bounded connected components of polynomial lemniscates

IF 1.4 3区数学 Q1 MATHEMATICS

Analysis and Mathematical Physics Pub Date : 2024-09-30 DOI:10.1007/s13324-024-00969-0

Adam Kraus, Brian Simanek

引用次数: 0

Abstract

We consider families of polynomial lemniscates in the complex plane and determine if they bound a Jordan domain. This allows us to find examples of regions for which we can calculate the projection of \(\bar{z}\) to the Bergman space of the bounded region. Such knowledge has applications to the calculation of torsional rigidity.

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多项式∞的有界连通分量

我们考虑复平面上的多项式∞族，并确定它们是否约束了一个约旦域。这样，我们就能找到一些区域的例子，从而计算出这些区域的 \(\bar{z}\) 对有界区域的伯格曼空间的投影。这些知识可以应用于扭转刚性的计算。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

0.00%

发文量

122

期刊介绍： Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.