Title

On the use of green's function in sampling theory

Keywords

Boundary-value problems; Kramer's sampling theorem

Abstract

There are many papers dealing with Kramer's sampling theorem associated with self-adjoint boundary-value problems with simple eigenvalues. To the best of our knowledge, Zayed was the first to introduce a theorem that deals with Kramer's theorem associated with Green's function of not necessarily self-adjoint problems which may have multiple eigenvalues, but no examples of sampling series associated with either non-self-adjoint problems or problems with multiple eigenvalues were given. We define two classes of not necessarily self-adjoint problems for which sampling theorems can be derived and give a sampling theorem associated with Green's function of self-adjoint problems. Finally, we give some examples that illustrate our technique. © 1998 Rocky Mountain Mathematics Consortium.

Publication Date

12-1-1998

Publication Title

Journal of Integral Equations and Applications

Volume

10

Issue

2

Number of Pages

117-139

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1216/jiea/1181074218

Socpus ID

0000738719 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0000738719

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