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The product of the distributions and

Published online by Cambridge University Press:  24 October 2008

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

In the following a distribution or a generalized function f is denned, as by Gelfand and Shilov(2) or by Temple (3), as a continuous linear functional on the space K of infinitely differentiable test functions ø having compact support. The value of f at a test function ø will be denoted by (f, ø).

A sequence of test functions {øn} is said to be a null sequence if

(1) the support of each øn is contained in some fixed domain D independent of n,

(2) the sequence converges uniformly to zero in D, as n tends to infinity, for all m.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 71 , Issue 1 , January 1972 , pp. 123 - 130
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

(1)Fisher, B.The product of distributions. Quart. J. Math. Oxford (2), 22 (1971), 291–8.CrossRefGoogle Scholar
(2)Gelfand, I. M. and Shilov, G. E.Generalized functions, Vol. I (1964).Google Scholar
(3)Temple, G.The theory of generalized functions. Proc. Boy. Soc. Ser. A 28 (1955), 175–190.Google Scholar