Jacobi polynomial expansions
type: Item
instance of: scholarly article
title: Jacobi polynomial expansions
zbMATH Open document ID: 0802.34087
author: Mojdeh Hajmirzaahmad
published in: Journal of Mathematical Analysis and Applications
publication date: 1994-12-13T00:00:00Z
review text: The paper is devoted to eigenfunction expansions associated with Jacobi polynomials \([^{\alpha,\beta} P_ n]^ \infty_{n=0}\). The classical expansion associated with the Jacobi operator is well-known when \(a>-1\), \(\beta> -1\). It is shown that when \(\alpha\), \(\beta<-1\), there are eigenfunction expansions associated with Jacobi operators and Jacobi polynomials, of course in a different function space which is a Sobolev space. It is shown that in this space, the Jacobi operator is self- adjoint. The eigenfunction expansions of the space remain valid for all \(\alpha\), \(\beta\) and are same as there in the \(L_ 2\)-space when \(\alpha\), \(\beta>-1\). Finally, it is shown that spectral resolution in the \(L_ 2\) space hold in the new space mentioned above.
Mathematics Subject Classification ID: 34L10
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 567023
zbMATH Keywords: eigenfunction expansions
zbMATH Keywords: Jacobi polynomials
zbMATH Keywords: spectral resolution
reviewed by: Mahadeb Dutta
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1004
OpenAlex ID: W2077876398
DOI: 10.1006/JMAA.1994.1004
description: scientific article; zbMATH DE number 567023