Quadrature domains packing

Fuente: arXiv
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Main Authors: Gustafsson, Bjorn, Putinar, Mihai
Format: Preprint
Published: 2024
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author Gustafsson, Bjorn
Putinar, Mihai
author_facet Gustafsson, Bjorn
Putinar, Mihai
contents Given a finite family of compact subsets of the complex plane we propose a certificate of mutual non-overlapping with respect to area measure. The criterion is stated as a couple of positivity conditions imposed on a four argument analytic/anti-analytic kernel defined in a neighborhood of infinity. In case the compact sets are closures of quadrature domains the respective kernel is rational, enabling an effective matrix analysis algorithm for the non-overlapping decision. The simplest situation of two disks is presented in detail from a matrix model perspective as well as from a Riemann surface potential theoretic interpretation.
format Preprint
id arxiv_https___arxiv_org_abs_2411_14124
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Quadrature domains packing
Gustafsson, Bjorn
Putinar, Mihai
Spectral Theory
Complex Variables
47B20, 30F15, 31A05, 52C15, 86A22
Given a finite family of compact subsets of the complex plane we propose a certificate of mutual non-overlapping with respect to area measure. The criterion is stated as a couple of positivity conditions imposed on a four argument analytic/anti-analytic kernel defined in a neighborhood of infinity. In case the compact sets are closures of quadrature domains the respective kernel is rational, enabling an effective matrix analysis algorithm for the non-overlapping decision. The simplest situation of two disks is presented in detail from a matrix model perspective as well as from a Riemann surface potential theoretic interpretation.
title Quadrature domains packing
topic Spectral Theory
Complex Variables
47B20, 30F15, 31A05, 52C15, 86A22
url https://arxiv.org/abs/2411.14124