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Open AccessArticle

Eigenvalue Problem for Discrete Jacobi–Sobolev Orthogonal Polynomials

1
Departamento de Matemáticas, Universidad de Almería, 04120 Almería, Spain
2
Instituto Carlos I de Física Teórica y Computacional, 18071 Granada, Spain
3
Department of Mathematics & Computer Science, Colorado College, CO 80903, USA
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(2), 182; https://doi.org/10.3390/math8020182
Received: 29 October 2019 / Revised: 7 January 2020 / Accepted: 22 January 2020 / Published: 3 February 2020
In this paper, we consider a discrete Sobolev inner product involving the Jacobi weight with a twofold objective. On the one hand, since the orthonormal polynomials with respect to this inner product are eigenfunctions of a certain differential operator, we are interested in the corresponding eigenvalues, more exactly, in their asymptotic behavior. Thus, we can determine a limit value which links this asymptotic behavior and the uniform norm of the orthonormal polynomials in a logarithmic scale. This value appears in the theory of reproducing kernel Hilbert spaces. On the other hand, we tackle a more general case than the one considered in the literature previously.
Keywords: Sobolev orthogonal polynomials; Jacobi weight; asymptotics Sobolev orthogonal polynomials; Jacobi weight; asymptotics
MDPI and ACS Style

Mañas-Mañas, J.F.; Moreno-Balcázar, J.J.; Wellman, A.R. Eigenvalue Problem for Discrete Jacobi–Sobolev Orthogonal Polynomials. Mathematics 2020, 8, 182.

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