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Some results on the product of distributions

Published online by Cambridge University Press:  24 October 2008

B. Fisher
B. Fisher
Affiliation:
Department of Mathematics, University of Leicester
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Extract

The product of two distributions f and g on the open interval (a, b), where −∞ ≤ a < b ≤ ∞, was defined(1) as the limit of the sequence {fngn}, provided this sequence is regular on (a, b), where

for n = 1, 2, … and ρ is a fixed infinitely differentiable function having the following properties:

(1) ρ(x) = 0 for |x| ≥ 1,

(2) ρ(x) ≥ 0,

(3) ρ(x) = ρ(−x),

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 73 , Issue 2 , March 1973 , pp. 317 - 325
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

(1)Fisher, B.The product of distributions. Quart. J. Math. Oxford Ser. 2 (1971), 291–8.CrossRefGoogle Scholar
(2)Mikusiński, J.On the square of the Dirac delta-distribution. Bull. A. Polon. Sci. Ser. Sci. Math. Astr. Phys. 14 (1966), 511–13.Google Scholar