Eigenvalue Problem for Discrete Jacobi–Sobolev Orthogonal Polynomials

Autor:	Juan F. Mañas-Mañas, Juan J. Moreno-Balcázar, Richard Wellman
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	sobolev orthogonal polynomials jacobi weight asymptotics Mathematics QA1-939
Zdroj:	Mathematics, Vol 8, Iss 2, p 182 (2020)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math8020182
Popis:	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.
Databáze:	Directory of Open Access Journals
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