Asymptotic behavior of orthogonal rational functions corresponding to measure with discrete part off the unit circle
type: Item
instance of: scholarly article
title: Asymptotic behavior of orthogonal rational functions corresponding to measure with discrete part off the unit circle
zbMATH Open document ID: 0878.42013
author: O. Diekmann
published in: Rocky Mountain Journal of Mathematics
publication date: 1997-11-20T00:00:00Z
full work available at URL: CONT26-4.html
review text: Consider two measures, \(\mu_1\) entirely supported on the unit circle, and \(\mu_2\) equal to \(\mu_1\) plus a finite number of mass points which lie off the unit circle. Consider the respective sequences of orthogonal rational functions \(\{\phi_n\}\) and \(\{\varphi_n\}\), with poles fixed along a Newtonian table of points. The author gives sufficient conditions on the measure \(\mu\) and the table of fixed poles in order that \(\frac{\varphi_n}{\phi_n}\) converge uniformly on compact subsets of the exterior of the unit circle as \(n\) tends to \(\infty\).
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 1036058
zbMATH Keywords: orthogonal rational functions
zbMATH Keywords: relative asymptotics
reviewed by: Guillermo López Lagomasino
MaRDI profile type: Publication
OpenAlex ID: W2036870486
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DOI: 10.1216/RMJM/1181072002
description: scientific article; zbMATH DE number 1036058