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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 Hindawi Publishing Corporation. 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.