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Differential and difference operators having orthogonal polynomials with two linear perturbations as eigenfunctions

✍ Scribed by H. Bavinck

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 463 KB
Volume: 92
Category: Article
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(98)00010-7

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✦ Synopsis

In this paper we consider the polynomials {P~'V(x)}~0, orthogonal with respect to a certain symmetric bilinear form of Sobolev type. These polynomials are the result of two linear perturbations to the orthogonal polynomials {Pn(x)}~0, eigenfunctions of a linear differential or difference operator L. We show that the polynomials {Pff'V(x)}~0 are eigenfunctions of one or more linear differential or difference operators (possibly of infinite order) of the form L + #A + vB +/~vC.

📜 SIMILAR VOLUMES

Linear perturbations of differential of

Linear perturbations of differential of difference operators with polynomials as eigenfunctions

✍ H. Bavinck 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 665 KB

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 differen