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support of tempered distributions

Proceedings of the Edinburgh Mathematical Society (1)

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1 results

On the support of tempered distributions
Part of
- Harmonic analysis in several variables
- Distributions, generalized functions, distribution spaces
Jasson Vindas, Ricardo Estrada
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 53 / Issue 1 / February 2010

Published online by Cambridge University Press:

12 January 2010, pp. 255-270
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We show that if the summability means in the Fourier inversion formula for a tempered distribution f ∈ S′(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.