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

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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.
Publisher
ROCKY MT MATH CONSORTIUM
Issue Date
2001
Language
English
Article Type
Article
Citation

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, v.31, no.3, pp.899 - 937

ISSN
0035-7596
URI
http://hdl.handle.net/10203/83781
Appears in Collection
MA-Journal Papers(저널논문)
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