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On the support of tempered distributions

Published online by Cambridge University Press:  12 January 2010

Jasson Vindas
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA, Email: ([email protected], [email protected])
Ricardo Estrada
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA, Email: ([email protected], [email protected])
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Abstract

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We show that if the summability means in the Fourier inversion formula for a tempered distribution fS′(ℝn) converge to zero pointwise in an open set Ω, and if those means are locally bounded in L1(Ω), then Ω ⊂ ℝn\supp f. We prove this for several summability procedures, in particular for Abel summability, Cesàro summability and Gauss-Weierstrass summability.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2010