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Eigenvalue Problem for Discrete Jacobi–Sobolev Orthogonal Polynomials

Author

Listed:
  • Juan F. Mañas-Mañas

    (Departamento de Matemáticas, Universidad de Almería, 04120 Almería, Spain
    These authors contributed equally to this work.)

  • Juan J. Moreno-Balcázar

    (Departamento de Matemáticas, Universidad de Almería, 04120 Almería, Spain
    Instituto Carlos I de Física Teórica y Computacional, 18071 Granada, Spain
    These authors contributed equally to this work.)

  • Richard Wellman

    (Department of Mathematics & Computer Science, Colorado College, CO 80903, USA
    These authors contributed equally to this work.)

Abstract

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.

Suggested Citation

  • Juan F. Mañas-Mañas & Juan J. Moreno-Balcázar & Richard Wellman, 2020. "Eigenvalue Problem for Discrete Jacobi–Sobolev Orthogonal Polynomials," Mathematics, MDPI, vol. 8(2), pages 1-19, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:182-:d:315791
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