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Generalized transforms and convolutions

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  • Timothy Huffman
  • Chull Park
  • David Skoug

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.

Suggested Citation

  • Timothy Huffman & Chull Park & David Skoug, 1997. "Generalized transforms and convolutions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 20, pages 1-14, January.
    • Handle: RePEc:hin:jijmms:126253
    DOI: 10.1155/S0161171297000045
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