International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 1, Pages 19-32
doi:10.1155/S0161171297000045
Generalized transforms and convolutions
Timothy Huffman1
, Chull Park2
and David Skoug3
1Department of Mathematics, Northwestern College, Orange City 51041, IA, USA
2Department of Mathematics and Statistics, Miami University, Oxford 45056, OH, USA
3Department of Mathematics and Statistics, University of Nebraska, Lincoln 68588, NE, USA
Abstract
In this paper, using the concept of a generalized Feynman integral, we define a generalized Fourier-Feynman transform and a generalized convolution product. Then for two classes of functionals on Wiener space we obtain several results involving and relating these generalized transforms and convolutions. In particular we show that the generalized transform of the convolution product is a product of transforms. In addition we establish a Parseval's identity for functionals in each of these classes.