International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 1, Pages 19-32
Generalized transforms and convolutions
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
Copyright © 1997 Timothy Huffman 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.
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.