Annihilating measures of the algebra R(X)
type: Item
instance of: scholarly article
title: Annihilating measures of the algebra R(X)
zbMATH Open document ID: 0551.46032
DOI: 10.1016/0022-1236(84)90038-7
published in: Journal of Functional Analysis
publication date: 1984-01-01T00:00:00Z
review text: We introduce a special class of ''analytic measures'' in the totality of measures orthogonal to the algebra of rational functions R(X) on a compact set \(X\subset {\mathbb{C}}.\) They are defined as weak* limits of the analytic differentials ''sitting'' on the boundaries of ''nice'' sets converging to X. We show that if \(R(X)\neq C(X),\) then there always exist non-trivial analytic measures. Moreover, if functions harmonic in the neighborhood of X are dense in \({\mathcal C}(\partial X)\), then measures are weak* dense in the space of all annihilating measures for R(X) concentrated on the boundary of X.
Mathematics Subject Classification ID: 46J15
Mathematics Subject Classification ID: 46E10
Mathematics Subject Classification ID: 28C05
zbMATH DE Number: 3877804
zbMATH Keywords: algebra of rational functions
zbMATH Keywords: Cauchy transform
zbMATH Keywords: analytic measures
zbMATH Keywords: analytic differentials
zbMATH Keywords: space of all annihilating measures
author: Dmitry Khavinson
MaRDI profile type: Publication
full work available at URL: 0022-1236(84)90038-7
OpenAlex ID: W2050369989
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description: scientific article; zbMATH DE number 3877804