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Zbl 1183.42011
On the support of tempered distributions.
(English)
[J] Proc. Edinb. Math. Soc., II. Ser. 53, No. 1, 255-270 (2010). ISSN 0013-0915; ISSN 1464-3839/e

Summary: We show that if the summability means in the Fourier inversion formula for a tempered distribution $f\in \cal S^{\prime}(\Bbb R^{n})$ converge to zero pointwise in an open set $\varOmega$, and if those means are locally bounded in $L^{1}(\varOmega)$, then $\varOmega \subset \Bbb R^{n}\setminus \text{ supp } f$. We prove this for several summability procedures, in particular for Abel summability, Cesàro summability and Gauss-Weierstrass summability.
MSC 2000:
*42B10 Fourier type transforms, several variables
46F10 Operations with distributions (generalized functions)
40C99 General summability methods

Keywords: support of tempered distributions; Fourier transforms; Cesàro summability; Abel summability; spherical means

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