Title

Kramer’s Sampling Theorem With Discontinuous Kernels

Keywords

discontinuous Sturm-Liouville problems; Shannon and Kramer sampling theorems; Sturm-Liouville problems

Abstract

Kramer’s sampling theorem provides an algorithm for reconstructing a function ƒ, in the form (Formual presented.) from its values at a discrete set of points. In all the known examples, the kernel of the transform, K(x,t) is continuous in x and entire in t, even though the proof of the theorem shows that the continuity in x is not essential. This raises the question of whether it is possible to find an example of Kramer’s theorem with a discontinuous kernel. The aim of the paper is to answer this question in the affirmative. We show how one can construct a family of discontinuous kernels for which Kramer’s theorem holds and, in addition, each member of this family arises from a Sturm-Liouville problem, but with discontinuous initial conditions.

Publication Date

8-1-1998

Publication Title

Results in Mathematics

Volume

34

Issue

1-2

Number of Pages

197-206

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/BF03322050

Socpus ID

0041697834 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0041697834

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