Universality in measure in the bulk for varying weights
type: Item
instance of: scholarly article
title: Universality in measure in the bulk for varying weights
zbMATH Open document ID: 1365.15044
author: Eli Levin
author: Doron S. Lubinsky
published in: Michigan Mathematical Journal
publication date: 2017-03-14T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.mmj/1480734022
review text: The authors deal with universality results in measure for sequences of varying weights \(\{g_{n} \exp (-2nQ)\},\) where \(\exp(-Q)\) is an exponential weight and \(g_{n}\) are functions which admit suitable polynomial approximations. It is assumed that \(Q\) is continuous while \(Q'\) is continuous up to a finitely number of points of the support of the measure that is constituted by finitely many compact intervals. It is also assumed that the equilibrium measure \(\omega_{Q}\) is absolutely continuous and \(\omega'_{Q}\) is positive and continuous in the interior of \(S_{Q},\) the support of \(\omega_{Q},\) up to at finitely many points. They extend a previous result by the authors [Adv. Math. 219, No. 3, 743--779 (2008; Zbl 1176.28014)] to varying weights whose proof depends heavily on asymptotics of Christoffel functions established in [\textit{V. Totik}, Adv. Appl. Math. 25, No. 4, 322--351 (2000; Zbl 0970.42016)]. The authors prove that universality holds in measure for weights under more general hypotheses than those of their previous contribution. First, they obtain a equiconvergence result (Theorem 1.1) and, as a consequence, the universality in measure to the sinc kernel follows. Potential theoretic estimates are used together with pointwise estimates in order to get Theorem 1.1.
reviewed by: Francisco Marcellán
Mathematics Subject Classification ID: 15B52
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 60B20
zbMATH DE Number: 6694759
zbMATH Keywords: varying weights
zbMATH Keywords: exponential weights
zbMATH Keywords: equlibrium measures
zbMATH Keywords: Christoffel functions
zbMATH Keywords: universality in measure
zbMATH Keywords: sinc kernel
MaRDI profile type: Publication
OpenAlex ID: W2558602982
DOI: 10.1307/MMJ/1480734022
description: scientific article; zbMATH DE number 6694759