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The support of tempered distributions

Published online by Cambridge University Press:  01 March 2008

Colin C. Graham
Colin C. Graham*
Affiliation:
Department of Mathematics, University of British ColumbiaMailing address: RR#1–D156, Bowen Island, BC, V0N 1G0Canada. e-mail: ccgraham@alum.mit.edu
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Abstract

We identify the support of a tempered distribution by evaluation of a sequence of test functions against the Fourier transform of the distribution. This improves previous results by removing the restriction that the distribution's Fourier transform be in and be of polynomial growth. We use an apparently new technical lemma that implies that certain bounded approximate identities for are also topological approximate identities for elements of the space of Schwartz functions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 144 , Issue 2 , March 2008 , pp. 495 - 498
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

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