On the strong asymptotics for Sobolev orthogonal polynomials on the circle
type: Item
instance of: scholarly article
title: On the strong asymptotics for Sobolev orthogonal polynomials on the circle
zbMATH Open document ID: 1015.42017
published in: Constructive Approximation
publication date: 2003-05-04T00:00:00Z
review text: The authors prove Szegős's asymptotic theorem for the orthogonal polynomials with respect to a Sobolev inner product of the following type \[ \langle f(z),g(z)\rangle_s= \sum^p_{k=0} \int^{2\pi}_0 f^{(k)}(e^{i\theta})\overline{g^{(k)}(e^{i\theta})} d\mu_k(\theta),\quad z= e^{i\theta}, \] with \(\mu_k\), \(k= 0,1,\dots, p-1\), finite positive Borel measures on \([0,2\pi]\) and \(\mu_p\) a measure in the Szegő class.
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33C47
zbMATH DE Number: 1903848
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: Sobolev inner products
zbMATH Keywords: Szegős's asymptotic theorem
author: E. Berriochoa
author: A. Cachafeiro
MaRDI profile type: Publication
full work available at URL: s00365-002-0517-y
OpenAlex ID: W155671968
DOI: 10.1007/S00365-002-0517-Y
description: scientific article; zbMATH DE number 1903848