We show that if the summability means in the Fourier inversion formula for a tempered distribution f [is an element of] S[variant prime]([DOUBLE-STRUCK CAPITAL R]n) converge to zero pointwise in an open set [Omega], and if those means are locally bounded in L1([Omega]), then [Omega] [subset or is implied by] [DOUBLE-STRUCK CAPITAL R]nsupp f. We prove this for several summability procedures, in particular for Abel summability, Cesàro summability and Gauss-Weierstrass summability. [PUBLICATION ABSTRACT]
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机译：我们证明，如果在调和分布f的傅里叶反演公式中的可加性平均值f [是] S [变质数]（[双重资本R] n的元素）在一个开放集合Ω中逐点收敛到零，如果这些均值在L1（ω）中局部有界，则Ω[子集或由[双重资本R] nsupp f隐含。我们通过几种可求性过程证明了这一点，特别是对于Abel可求性，Cesàro可求性和Gauss-Weierstrass可求性。 [出版物摘要]
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