A new proof of a theorem about generalized orthogonal polynomials
type: Item
instance of: scholarly article
title: A new proof of a theorem about generalized orthogonal polynomials
zbMATH Open document ID: 0729.42016
DOI: 10.1155/S0161171291000467
author: A. McD. Mercer
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46602
review text: Let \(\{p_ n\}\) \((n=0,1,2,...)\) be a sequence of polynomials orthonormal with respect to the measure \(\alpha\). The author gives an alternative proof of an important Nevai's theorem on the asymptotic distribution of the zeros of the polynomials \(\{p_ n\}\) \((n=0,1,2,...)\) by the aid of an old theorem of G. Pólya about the eigenvalues of the Toeplitz matrix.
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 26C10
zbMATH DE Number: 4205093
zbMATH Keywords: orthogonal polynomial
zbMATH Keywords: Nevai's theorem on the asymptotic distribution of the zeros
reviewed by: B. P. Osilenker
MaRDI profile type: Publication
OpenAlex ID: W2015783137
description: scientific article; zbMATH DE number 4205093