Real Algebraic Geometry of Real Algebraic Jordan Curves in the Plane and the Bergman Kernel

被引：0

作者：

Bell, Steven R. ^{[1
]}

机构：

[1] Purdue Univ, Math Dept, W Lafayette, IN 47907 USA

来源：

ANALYSIS MATHEMATICA | 2022年 / 48卷 / 02期

关键词：

Poisson kernel; Bergman kernel; Schwarz function; QUADRATURE IDENTITIES; DOMAINS;

D O I：

10.1007/s10476-022-0139-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We characterize the space of restrictions of real rational functions to certain algebraic Jordan curves in the plane via the Dirichlet-to-Neumann map associated to the domain in the complex plane bounded by the curve and its Bergman kernel. The characterization leads to a partial fractions-like decomposition for such rational functions and new ways to describe such Jordan curves. The multiply connected case is also explored.

引用

页码：331 / 345

页数：15