International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 5, Pages 301-317

On the finite Fourier transforms of functions with infinite discontinuities

Branko Saric

The Institute “Kirilo Savic“, V. Stepe 51, Belgrade 11000, Serbia

Received 2 April 2001

Copyright © 2002 Branko Saric. 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 introductory part of the paper is provided to give a brief review of the stability theory of a matrix pencil for discrete linear time-invariant singular control systems, based on the causal relationship between Jordan's theorem from the theory of Fourier series and Laurent's theorem from the calculus of residues. The main part is concerned with the theory of the integral transforms, which has proved to be a powerful tool in the control systems theory. On the basis of a newly defined notion of the total value of improper integrals, throughout the main part of the paper, an attempt has been made to present the global theory of the integral transforms, which are slightly more general with respect to the Laplace and Fourier transforms. The paper ends with examples by which the results of the theory are verified.