On the support of tempered distributions
Jasson VindasDepartment of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA, Email:Ricardo EstradaDepartment of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA, Email:
2010en
ABI
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.
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Cited by 30 references