Eigenvalue Problem for Discrete Jacobi–Sobolev Orthogonal Polynomials

Mathematics

JuanJ. Moreno-Balcázar¹  JuanF. Mañas-Mañas¹  Richard Wellman² 

[1] Departamento de Matemáticas, Universidad de Almería, 04120 Almería, Spain;;Department of Mathematics &

关键词: sobolev orthogonal polynomials;    jacobi weight;    asymptotics;   

DOI  :  10.3390/math8020182

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown