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Fractional convolution

Published online by Cambridge University Press:  17 February 2009

David Mustard
David Mustard
Affiliation:
School of Mathematics, University of New South Wales, Sydney, Australia2052.
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Abstract

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A continuous one-parameter set of binary operators on L2(R) called fractional convolution operators and which includes those of multiplication and convolution as particular cases is constructed by means of the Condon-Bargmann fractional Fourier transform. A fractional convolution theorem generalizes the standard Fourier convolution theorems and a fractional unit distribution generalizes the unit and delta distributions. Some explicit double-integral formulas for the fractional convolution between two functions are given and the induced operation between their corresponding Wigner distributions is found.

Type
Research Article
Information
The ANZIAM Journal , Volume 40 , Issue 2 , October 1998 , pp. 257 - 265
Copyright
Copyright © Australian Mathematical Society 1998

References

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