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A note on the Fourier transform of generalized functions

Published online by Cambridge University Press:  24 October 2008

B. Fisher
B. Fisher
Affiliation:
University of Leicester
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Extract

If F(f) denotes the Fourier transform of a generalized function f and f * g denotes the convolution product of two generalized functions f and g then it is known that under certain conditions

Jones (2) states that this is not true in general and gives as a counter-example the case when f = g = H, H denoting Heaviside's function. In this case

and the product (x−1 – iπδ)2 is not defined in his development of the product of generalized functions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 70 , Issue 1 , July 1971 , pp. 49 - 51
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

REFERENCES

(1)Fisher, B.The generalized function (x + i0)λ. Proc. Cambridge Philoe. Soc. 68 (1970), 707.CrossRefGoogle Scholar
(2)Jones, D. S.Generalised functions (McGraw-Hill, 1966).Google Scholar