Self-adjoint operators generated from non-Lagrangian symmetric equations having orthogonal polynomial eigenfunctions

W Everitt, KH Kwon, JK Lee, LL Littlejohn, SC Williams

Research output: Contribution to journalArticle

Abstract

We discuss the self-adjoint spectral theory associated with a certain fourth-order non-Lagrangian symmetrizable ordinary differential equation t(4)[y] = lambday that has a sequence of orthogonal polynomial solutions. This example was first discovered by Jung, Kwon, and Lee. In their paper, they derive the remarkable formula for these polynomials {Q(n)(x)}(n=0)infinity : Q(n)(x) = n integral(1)(x) PLn-1(t)dt, n is an element of N, where {PLn(x)}(n=0)(infinity) are the left Legendre type polynomials. The left Legendre type polynomials and the spectral analysis of the associated symmetric fourth-order differential equation that they satisfy have been extensively studied previously by Krall, Loveland, Everitt, and Littlejohn.
Original languageEnglish
Pages (from-to)899-937
Number of pages39
JournalRocky Mountain Journal of Mathematics
Volume31
DOIs
Publication statusPublished - 1 Sep 2001

Fingerprint

Dive into the research topics of 'Self-adjoint operators generated from non-Lagrangian symmetric equations having orthogonal polynomial eigenfunctions'. Together they form a unique fingerprint.

Cite this