Uniform approximation on Riemann surfaces by holomorphic and harmonic functions
type: Item
instance of: scholarly article
title: Uniform approximation on Riemann surfaces by holomorphic and harmonic functions
zbMATH Open document ID: 1040.30020
published in: Illinois Journal of Mathematics
publication date: 2004-01-19T00:00:00Z
review text: Let \(K\) be a compact subset of an open Riemann surface. We prove that if \(L\) is a peak set for \(A(K)\), then \(A(K)| L=A(L)\). We also prove that if \(E\) is a compact subset of \(K\) with no interior such that each component of \(E^c\) intersects \(K^c\), then \(A(K)| E\) is dense in \(C(E)\). One consequence of the latter result is a characterization of the real-valued continuous functions that when adjoined to \(A(K)\) generate \(C(K)\).
reviewed by: Gerald Schmieder
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 30F99
zbMATH DE Number: 2028861
author: Boju Jiang
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2028861