International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 2, Pages 355-358

The generalized sampling theorem for transforms of not necessarily square integrable functions

A. J. Jerri

Department of Mathematics and Computer Science, Clarkson College of Technology, Potsdam 13676, N.Y., USA

Received 1 February 1982

Copyright © 1985 A. J. Jerri. 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.


It is known that the generalized sampling theorem is valid for certain finite limit integral transforms of square integrable functions. In this note, we will extend the validity of the theorem to include transforms of absolutely integrable functions associated with differentiable kernels. In the proof, we will use the Hölder inequality and a known theorem concerning the uniform convergence of the orthogonal series to the differentiable kernel of the particular integral transform.