Orthogonal polynomials associated with the Dirac operator in Euclidean space
type: Item
instance of: scholarly article
title: Orthogonal polynomials associated with the Dirac operator in Euclidean space
zbMATH Open document ID: 0751.33002
published in: Chinese Annals of Mathematics. Series B
publication date: 1992-09-27T00:00:00Z
review text: This paper deals with a method of generalizing the theory of classical orthogonal polynomials to the higher dimensional cases. The second order differential operator of these polynomials is split into the derivation operator, considered as an operator between Hilbert spaces and its adjoint. In the case of higher dimensions the derivation operator is replaced by the Dirac operator. Jacobi polynomials, thereby Gegenbauer, Chebyshev and Legendre polynomials, Laguerre and Hermite polynomials are generalized to higher dimensions.
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 34K30
zbMATH DE Number: 60826
zbMATH Keywords: Laguerre polynomial
zbMATH Keywords: Hermite polynomial
zbMATH Keywords: classical orthogonal polynomials
zbMATH Keywords: second order differential operator
zbMATH Keywords: Hilbert spaces
zbMATH Keywords: derivation operator
zbMATH Keywords: Dirac operator
zbMATH Keywords: Jacobi polynomials
zbMATH Keywords: higher dimensions
author: J. Cnops
reviewed by: Arakaparampil M. Mathai
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 60826