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The product of the distributions x−r and δ(r−1)(x)

Published online by Cambridge University Press:  24 October 2008

B. Fisher
B. Fisher
Affiliation:
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 in (1) as the limit of the sequence {fn·gn} provided this sequence is regular in (a, b), where

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

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 2 , September 1972 , pp. 201 - 204
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

(1)Fisher, B.The product of distributions. Quart. J. Math. Oxford, Ser. 2, 22 (1971), 291–298.CrossRefGoogle Scholar
(2)Fisher, B.The product of the distributions and : Proc. Cambridge Philos. Soc. 71 (1972), 123–130.CrossRefGoogle Scholar