International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 11, Pages 579-598
doi:10.1155/S0161171204305260

Integral transforms, convolution products, and first variations

Bong Jin Kim,1 Byoung Soo Kim,2 and David Skoug3

1Department of Mathematics, Daejin University, Pocheon 487-711, South Korea
2University College, Yonsei University, Seoul 120-749, South Korea
3Department of Mathematics, University of Nebraska-Lincoln, Lincoln 68588-0323, NE, USA

Received 21 May 2003

Copyright © 2004 Bong Jin Kim 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.

Abstract

We establish the various relationships that exist among the integral transform ℱα,βF, the convolution product (F∗G)α, and the first variation δF for a class of functionals defined on K[0,T], the space of complex-valued continuous functions on [0,T] which vanish at zero.