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A result on the convolution of distributions

Published online by Cambridge University Press:  20 January 2009

B. Fisher
B. Fisher
Affiliation:
University of Leicester
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In a recent paper (1), Jones extended the definition of the convolution of two distributions to cover certain pairs of distributions which could not be convolved in the sense of the previous definition. The convolution ω1 * ω2 of two distributions ω1 and ω2 was defined as the limit of the sequence ω1n * ω2n, provided the limit ω exists in the sense that

for all fine functions φ in the terminology of Jones (2) where

and τ is an infinitely differentiate function satisfying the following conditions:

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 19 , Issue 4 , September 1975 , pp. 393 - 395
Copyright
Copyright © Edinburgh Mathematical Society 1975

References

REFERENCES

(1) Jones, D. S., The convolution of generalized functions, Quart. J. of Math. Oxford Ser. (2) 24 (1973), 145–163.CrossRefGoogle Scholar
(2) Jones, D. S., Generalized functions (McGraw-Hill, 1966).Google Scholar