Bounded point evaluations for nonminimal measures
type: Item
instance of: scholarly article
title: Bounded point evaluations for nonminimal measures
zbMATH Open document ID: 0657.31003
DOI: 10.1016/0022-1236(87)90024-3
author: Stephen L. Anderson
published in: Journal of Functional Analysis
publication date: 1987-01-01T00:00:00Z
review text: A compactly supported positive measure \(\sigma\) in the complex plane \({\mathbb{C}}\) is said to be nonminimal if there is a compactly supported positive measure \(\mu\), not equal to \(\sigma\), with logarithmic potential equal to the logarithmic potential of \(\sigma\) outside some compact set and less than or equal to the logarithmic potential of \(\sigma\) on \({\mathbb{C}}\). If \(\sigma\) is a nonminimal measure then there is a nonempty open set, \(\Omega\), such that every sequence of polynomials converging in \(L^ 2(\sigma)\) converges normally on \(\Omega\).
Mathematics Subject Classification ID: 31A15
zbMATH DE Number: 4073400
zbMATH Keywords: compactly supported positive measure
zbMATH Keywords: complex plane
zbMATH Keywords: nonminimal
zbMATH Keywords: logarithmic potential
MaRDI profile type: Publication
full work available at URL: 0022-1236(87)90024-3
OpenAlex ID: W2085828020
cites work: Green's function, Jensen measures, and bounded point evaluations
cites work: Point evaluations, invariant subspaces and approximation in the mean by polynomials
cites work: Mergelyan's Theorem on Uniform Polynomial Approximation.
cites work: Q3930259
description: scientific article; zbMATH DE number 4073400