Recurrence coefficients of orthogonal polynomials with respect to some self-similar singular distributions
type: Item
instance of: scholarly article
title: Recurrence coefficients of orthogonal polynomials with respect to some self-similar singular distributions
zbMATH Open document ID: 0820.42010
DOI: 10.4171/ZAA/667
author: Hans-Jürgen Fischer
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1995-06-13T00:00:00Z
review text: Monic orthogonal polynomials \(P_ n\) with orthogonality measure on \({\mathbf R}\) satisfy a 3-term recurrence relation \[ P_ n(x)= (x- c_ n) P_{n- 1}(x)- \lambda_ n P_{n- 2}(x)\quad (n\geq 1). \] The limit behavior of the arithmetic and geometric means of the coefficients \(c_ n\) and \(\lambda_ n\) is investigated. It is not assumed that the orthogonality measure is absolutely continuous, but regular \(n\)th root asymptotic behavior of the orthogonal polynomials \(P_ n\) must be guaranteed. Some examples of self-similar distributions satisfying this condition are given.
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 739098
zbMATH Keywords: three-term recurrence relations
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: orthogonality measure
zbMATH Keywords: self-similar distributions
reviewed by: Herbert Stahl
MaRDI profile type: Publication
cites work: Q3483795
cites work: A note on the zero distribution of orthogonal polynomials
cites work: Orthogonal polynomials
cites work: Q3473617
full work available at URL: https://doi.org/10.4171/zaa/667
OpenAlex ID: W1997884382
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description: scientific article; zbMATH DE number 739098