Abstract.
We show that, given a tempered distribution S whose Fourier transform is a function of polynomial growth, a point x in \({\mathbb{R}^{n}}\) is outside the support of S if and only if the Fourier integral of S is summable in Bochner-Riesz means to zero uniformly on a neighbourhood of x.
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Received: 29 December 2005
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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González Vieli, F.J., Graham, C.C. On the support of tempered distributions. Arch. Math. 88, 133–142 (2007). https://doi.org/10.1007/s00013-006-1852-1
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DOI: https://doi.org/10.1007/s00013-006-1852-1