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 , and if those means are locally bounded in L 1(Ω), then Ω ⊂ ℝn\supp f. We prove this for several summability procedures, in particular for Abel summability, Cesro summability and Gauss-Weierstrass summability. © 2010 Edinburgh Mathematical Society.
Publication Source (Journal or Book title)
Proceedings of the Edinburgh Mathematical Society
Vindas, J., & Estrada, R. (2010). On the support of tempered distributions. Proceedings of the Edinburgh Mathematical Society, 53 (1), 255-270. https://doi.org/10.1017/S0013091508000102