International Journal of Mathematics and Mathematical Sciences 
Volume 20 (1997), Issue 1, Pages 19-32
doi:10.1155/S0161171297000045

Generalized transforms and convolutions

Timothy Huffman,1 Chull Park,2 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
Received 27 June 1995; Revised 8 August 1995

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.