On the support of tempered distributions

Jasson Vindas, Ricardo Estrada

Type: Article

Publication Date: 2010-01-12

Citations: 16

DOI: https://doi.org/10.1017/s0013091508000102

Abstract

Abstract We show that if the summability means in the Fourier inversion formula for a tempered distribution f ∈ S ′(ℝ n ) converge to zero pointwise in an open set Ω, and if those means are locally bounded in L 1 (Ω), then Ω ⊂ ℝ n \supp f . We prove this for several summability procedures, in particular for Abel summability, Cesàro summability and Gauss-Weierstrass summability.

Locations

Proceedings of the Edinburgh Mathematical Society - View - PDF
Ghent University Academic Bibliography (Ghent University) - View - PDF

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+ PDF Chat	Characterization of the Fourier series of a distribution having a value at a point	1996	Ricardo Estrada
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