International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 11, Pages 709-715

On the analytic form of the discrete Kramer sampling theorem

Antonio G. García,1 Miguel A. Hernández-Medina,2 and María J. Muñoz-Bouzo3

1Departamento de Matemáticas, Universidad Carlos III de Madrid, Avda de la Universidad, 30, Leganés-Madrid 28911, Spain
2Departamento de Matemática Aplicada, E.T.S.I.T. Universidad Politécnica de Madrid, Avda Complutense s/n, Madrid 28040, Spain
3Departamento de Matemáticas Fundamentales, Facultad de Ciencias, U.N.E.D., Senda del Rey, 9, Madrid 28040, Spain

Received 15 March 2000; Revised 15 March 2000

Copyright © 2001 Antonio G. García et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The classical Kramer sampling theorem is, in the subject of self-adjoint boundary value problems, one of the richest sources to obtain sampling expansions. It has become very fruitful in connection with discrete Sturm-Liouville problems. In this paper a discrete version of the analytic Kramer sampling theorem is proved. Orthogonal polynomials arising from indeterminate Hamburger moment problems as well as polynomials of the second kind associated with them provide examples of Kramer analytic kernels.