TY - JOUR

T1 - Self-adjoint operators generated from non-Lagrangian symmetric equations having orthogonal polynomial eigenfunctions

AU - Everitt, W

AU - Kwon, KH

AU - Lee, JK

AU - Littlejohn, LL

AU - Williams, SC

PY - 2001/9/1

Y1 - 2001/9/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0035437987&partnerID=8YFLogxK

U2 - 10.1216/rmjm/1020171672

DO - 10.1216/rmjm/1020171672

M3 - Article

VL - 31

SP - 899

EP - 937

JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

ER -