Division problem of a regular form: the case \(x^2u=\lambda xv\)
type: Item
instance of: scholarly article
title: Division problem of a regular form: the case \(x^2u=\lambda xv\)
zbMATH Open document ID: 1220.39021
DOI: 10.1155/2011/794593
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2011-07-22T00:00:00Z
review text: Summary: We present a systematic study of a regular linear functional \(v\) to find all regular forms \(u\) which satisfy the equation \(x^{2}u = \lambda xv\), \(\lambda \in \mathbb C - \{ 0 \}\). We also give the second-order recurrence relation of the orthogonal polynomial sequence with respect to \(u\) and study the semiclassical character of the found families. We conclude by treating some examples.
Mathematics Subject Classification ID: 39B32
Mathematics Subject Classification ID: 39A45
zbMATH DE Number: 5930225
zbMATH Keywords: second-order recurrence relation
zbMATH Keywords: orthogonal polynomial sequence
Wikidata QID: Q58687947
author: M. Mejri
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/794593
OpenAlex ID: W2070800847
cites work: Q4170993
cites work: Delta perturbation of a moment functional
cites work: On a regular form defined by a pseudo-function
cites work: On the inverse problem of the product of a form by a polynomial: The cubic case.
cites work: On the inverse problem of the product of a form by a monomial: the casen=4. Part I
cites work: Division problem of moment functionals.
cites work: On rational transformations of linear functionals: direct problem
cites work: Modifications of quasi-definite linear functionals via addition of delta and derivatives of delta Dirac functions.
cites work: On the assignment of a Dirac-mass for a regular and semi-classical form
cites work: The product of a regular form by a polynomial generalized: the case \(xu = \lambda x^2 v\)
cites work: Sur la suite de polynômes orthogonaux associée à la forme \(u=\delta_ c+\lambda (x-c)^{-1}L\). (On the sequence of orthogonal polynomials associated with the form \(u=\delta_ c+\lambda (x-c)^{- 1}L)\)
cites work: On semi-classical linear functionals of class \(s=1\). Classification and integral representations
cites work: Q4853625
cites work: THE MATHEMATICS OF PRINCIPAL VALUE INTEGRALS AND APPLICATIONS TO NUCLEAR PHYSICS, TRANSPORT THEORY, AND CONDENSED MATTER PHYSICS
cites work: A Generalization of the Cauchy Principal Value
cites work: On Quasi-Orthogonal Polynomials
cites work: Q4843461
cites work: Semi-classical character and finite-type relations between polynomial sequences
cites work: On the linear functionals associated to linearly related sequences of orthogonal polynomials
cites work: Variations around classical orthogonal polynomials. Connected problems
cites work: Some semi-classical and Laguerre-Hahn forms defined by pseudo-functions
cites work: Some new results about a set of semi-classical polynomials of classs=1
cites work: The second-order self-associated orthogonal sequences
description: scientific article; zbMATH DE number 5930225