Characterization of polynomials via a raising operator
type: Item
instance of: scholarly article
title: Characterization of polynomials via a raising operator
zbMATH Open document ID: 1543.33008
author: Jihad Souissi
published in: Problemy Analiza. Issues of Analysis
publication date: 2024-05-15T00:00:00Z
review text: \textit{B. Aloui} [Period. Math. Hung. 76, 126--132 (2018; Zbl. 1413.33013)] proved that the scaled Chebyshev polynomial sequence is the only monic orthogonal polynomial sequence which is \( U_{\xi} \)-classical, i.e., for which the application of the raising operator \(U_{\xi}=x(xD+\mathbb{I})+\xi D, \) \( \xi\neq 0 \), turns the orthogonal sequence into another orthogonal one. Here the author proves a generalization of this result for the raising operator \( \mathcal{J}_{\xi}=x(xD+\mathbb{I})+\xi_1\mathbb{I}+\xi_2 D. \)
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 33E30
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 34L40
zbMATH DE Number: 7849906
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: classical polynomials
zbMATH Keywords: second-order differential equation
zbMATH Keywords: raising operator
MaRDI profile type: Publication
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DOI: 10.15393/J3.ART.2024.14050
description: scientific article; zbMATH DE number 7849906