The quasi-orthogonality of the derivatives of semi-classical polynomials
type: Item
instance of: scholarly article
title: The quasi-orthogonality of the derivatives of semi-classical polynomials
zbMATH Open document ID: 1024.42012
DOI: 10.1016/S0019-3577(02)80016-7
author: J. C. Medem
published in: Indagationes Mathematicae. New Series
publication date: 2003-11-11T00:00:00Z
review text: The distributional equation of a semi-classical functional provides an efficient way to study the properties of the semi-classical OPS/functionals. A particular case of semi-classical OPS/functionals are the classical ones, when a regularity condition holds for the distributional equation. It was shown earlier by the author that in general such condition does not hold. The main goal of the present paper is to analyze the consequences of the failure of regularity in the quasi-orthogonality of the derivatives of the semi-classical OPS. This study leads the author to the coprimality condition.
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33E30
zbMATH DE Number: 1893651
zbMATH Keywords: semi-classical functionals and orthogonal polynomials
zbMATH Keywords: distributional equation
zbMATH Keywords: quasi-orthogonality
zbMATH Keywords: regularity condition
zbMATH Keywords: coprimality condition
reviewed by: Leonid Golinskii
MaRDI profile type: Publication
cites work: Q4170993
cites work: Q3712910
cites work: On certain determinants whose elements are orthogonal polynomials
cites work: Classical orthogonal polynomials: A functional approach
cites work: Prolégomènes à l'étude des polynômes orthogonaux semi- classiques. (Preliminary remarks for the study of semi-classical orthogonal polynomials)
cites work: Q4853625
cites work: Variations around classical orthogonal polynomials. Connected problems
description: scientific article; zbMATH DE number 1893651