The support of the equilibrium measure for a class of external fields on a finite interval.
type: Item
instance of: scholarly article
title: The support of the equilibrium measure for a class of external fields on a finite interval.
zbMATH Open document ID: 1062.31002
published in: Pacific Journal of Mathematics
publication date: 2003-02-12T00:00:00Z
review text: The determination of the support of the equilibrium in the external field is a key step in the solution of many extremal problems in analysis. Unfortunately, it is also an essentially non-trivial one. There are not so many general results describing the properties of the support in terms of the equilibrium compact or the external field. Some of them are well known (for instance, when a convex and smooth external field is acting on the real line). One of the main results of this paper is a rather general sufficient condition on the external field on an interval ensuring that the support of the corresponding equilibrium measure is the union of at most two intervals. It is applied further to a non-smooth analogue of a monomial field of the form \(Q(x)=-c \, \text{sign}(x) | x| ^\alpha \), with \(c>0\) and \(\alpha \geq 1\), satisfying the conditions of the main theorem.
Mathematics Subject Classification ID: 31A15
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 1867907
zbMATH Keywords: logarithmic potential
zbMATH Keywords: equilibrium measure
zbMATH Keywords: external field
zbMATH Keywords: balayage
author: S. B. Damelin
author: P. D. Dragnev
author: Arno B. J. Kuijlaars
reviewed by: Andrei Martínez Finkelshtein
MaRDI profile type: Publication
OpenAlex ID: W2029043779
DOI: 10.2140/PJM.2001.199.303
description: scientific article; zbMATH DE number 1867907