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Linear perturbations of differential of difference operators with polynomials as eigenfunctions

โœ Scribed by H. Bavinck

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
665 KB
Volume
78
Category
Article
ISSN
0377-0427

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โœฆ Synopsis

This paper deals with one-parameter linear perturbations of a family of polynomials {Pn(x)}~0 with deg[P.(x)] = n of the form P~'(x) = Pn(x) +/~Q.(x), where p is a real parameter and {Qn(x)}~ 0 are polynomials with deg[Qn(x)] ~< n. Let the polynomials {Pn(x)}~0 be eigenfunctions of a linear differential or difference operator L with eigenvalues {2n}~0. The purpose of this paper is to derive necessary and sufficient conditions for the polynomials {Q.(x)}.~0 such that the polynomials {P~(x)}~0 are eigenfunctions of a linear difference or differential operator (possibly of infinite order) of the form L + I~A with eigenvalues

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