Erdös-Turán-type theorems on piecewise smooth curves and arcs
type: Item
instance of: scholarly article
title: Erdös-Turán-type theorems on piecewise smooth curves and arcs
zbMATH Open document ID: 0873.31004
author: H.-P. Blatt
author: V. V. Andrievskii
published in: Journal of Approximation Theory
publication date: 1997-04-08T00:00:00Z
review text: Let \(\sigma\) be a signed measure on a Jordan curve \(L\), then \(\sup|\sigma (J)|\) -- here the supremum is taken over all measurable subarcs \(J\) of \(L\) -- is called the discrepancy of \(\sigma\) on \(L\); further let \(\mu_L\) be the equilibrium measure on \(L\). Let \(p\) be a monic polynomial of degree \(n\) and let \(\nu_p\) be the corresponding normalized zero counting measure. For a piecewise smooth \(L\) the authors prove upper estimates of \(\sigma=\mu_L- \nu_p\) in terms of the logarithmic potential associated to \(\sigma\). As an application they obtain well-known results on Fekete points and extremal points of best uniform approximants.
Mathematics Subject Classification ID: 31A15
Mathematics Subject Classification ID: 30C85
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 980683
zbMATH Keywords: zeros of polynomials
zbMATH Keywords: Fekete points
zbMATH Keywords: extremal points
reviewed by: Klaus Menke
MaRDI profile type: Publication
full work available at URL: jath.1996.3015
OpenAlex ID: W2061663685
DOI: 10.1006/JATH.1996.3015
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description: scientific article; zbMATH DE number 980683