Finitely generated function fields and complexity in potential theory in the plane
type: Item
instance of: scholarly article
title: Finitely generated function fields and complexity in potential theory in the plane
zbMATH Open document ID: 0948.30015
DOI: 10.1215/S0012-7094-99-09805-8
author: Steven R. Bell
published in: Duke Mathematical Journal
publication date: 2000-03-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/9804060
review text: On an \(n\)-connected domain \(\Omega\) such that no boundary component is a point, the author shows that the Bergman kernel \(K(z,w)\) associated to \(\Omega\) is a rational combination of only three basic functions of one complex variable. That is, \(K(z,w)=R(f_a(z)\), \(f_a'(z)\), \(K(z,b)\), \(\overline{f_a(w)}\), \(\overline{f_a'(w)}\), \(\overline{K(w,b)})\) where \(R\) is a rational function on \(\mathbb{C}^6\), \(f_a\) is an Ahlfors map (which is a branched \(n\)-to-one covering map of \(\Omega\) onto the unit disc with \(f_a(a)=0\) and \(f_a'(a)>0\) and maximal), and \(a\) and \(b\) are fixed points in \(\Omega\).
Mathematics Subject Classification ID: 30C40
Mathematics Subject Classification ID: 31-XX
zbMATH DE Number: 1425214
zbMATH Keywords: \(n\)-connected domain
zbMATH Keywords: national function
zbMATH Keywords: Bergman kernel
reviewed by: Takahiko Nakazi
MaRDI profile type: Publication
arXiv ID: math/9804060
cites work: Q5593095
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description: scientific article