International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 9-12, Pages 579-598
doi:10.1155/S0161171204305260
Integral transforms, convolution products, and first variations
Bong Jin Kim1
, Byoung Soo Kim2
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
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.