A family of singular semi-classical functionals
type: Item
instance of: scholarly article
title: A family of singular semi-classical functionals
zbMATH Open document ID: 1031.42025
DOI: 10.1016/S0019-3577(02)80015-5
author: J. C. Medem
published in: Indagationes Mathematicae. New Series
publication date: 2003-07-15T00:00:00Z
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. For the distributional equation of classical functionals a regularity condition holds. The main result of the present paper is to show that in general such condition does not hold. The examples of semi-classical functionals that satisfy certains singular equation are built and an explicit representation of the corresponding monic orthogonal polynomials as well as the recurrence relations are found.
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33E30
zbMATH DE Number: 1893650
zbMATH Keywords: semi-classical functionals
zbMATH Keywords: distributional equation
zbMATH Keywords: quasi-orthogonality
zbMATH Keywords: regularity condition
zbMATH Keywords: admissibility condition
zbMATH Keywords: orthogonal polynomials
reviewed by: Leonid Golinskii
MaRDI profile type: Publication
cites work: Symmetric laguerre-hahn forms of classs=1
cites work: On semi-classical linear functionals of class \(s=1\). Classification and integral representations
cites work: Q4170993
cites work: Classical orthogonal polynomials: A functional approach
cites work: Q4853625
cites work: Variations around classical orthogonal polynomials. Connected problems
cites work: The quasi-orthogonality of the derivatives of semi-classical polynomials
description: scientific article; zbMATH DE number 1893650