Differential equations and Sobolev orthogonality

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Consider (Sobolev) orthogonal polynomials which are orthogonal relative to a Sobolev bilinear form integral(R) p(x)q(x)d mu(x) + integral(R) p'(x)q'd nu(x), where d mu(x) and d nu(x) are signed Borel measures with finite moments. We give necessary and sufficient conditions under which such orthogonal polynomials satisfy a linear spectral differential equation with polynomial coefficients. We then find a sufficient condition under which such a differential equation is symmetrizable. These results can be applied to Sobolev-Laguerre polynomials found by Koekoek and Meijer.
Publisher
ELSEVIER SCIENCE BV
Issue Date
1995-12
Language
English
Article Type
Article; Proceedings Paper
Keywords

POLYNOMIALS

Citation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, v.65, no.1-3, pp.173 - 180

ISSN
0377-0427
URI
http://hdl.handle.net/10203/73769
Appears in Collection
MA-Journal Papers(저널논문)
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