Journal
JOURNAL OF SPECTRAL THEORY
Volume 8, Issue 1, Pages 191-234Publisher
EUROPEAN MATHEMATICAL SOC
DOI: 10.4171/JST/194
Keywords
Orthogonal polynomials; differential operators and equations; Jacobi polynomials; Krall polynomials
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Funding
- Ministerio de Economia y Competitividad [MTM2012-36732-C03-03]
- Junta de Andalucia [FQM-262, FQM-4643, FQM-7276]
- Feder Funds (European Union)
- PAPIIT-DGAPA-UNAM (Mexico) [IA100515]
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The aim of this paper is to study differential properties of orthogonal polynomials with respect to a discrete Jacobi-Sobolev bilinear form with mass point at -1 and/or +1. In particular, we construct the orthogonal polynomials using certain Casorati determinants. Using this construction, we prove that when the Jacobi parameters alpha and beta are nonnegative integers the Jacobi-Sobolev orthogonal polynomials are eigenfunctions of a differential operator of finite order (which will be explicitly constructed). Moreover, the order of this differential operator is explicitly computed in terms of the matrices which define the discrete Jacobi-Sobolev bilinear form.
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