Abstract
Using \(p\)-adic distributions we obtain the uniqueness result for convolution. As a corollary of this result one can obtain \(p\)-adic Wiener Tauberian theorem and Wiener approximation theorem. Also we prove that there is no basis of \(L^1(\mathbb Q^n_p)\) consisting of translates of a function.
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Acknowledgments
The author thanks the anonymous referee whose critical remarks change the content of the paper.
Funding
This work is supported by the Ministry of Science and Education of the Russian Federation in the framework of the basic part of the scientific research state task, project FSRR-2020-0006.
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Volosivets, S.S. A Distributional Proof of \(p\)-Adic Wiener Tauberian Theorem and Approximation by Translates of a Function. P-Adic Num Ultrametr Anal Appl 13, 308–315 (2021). https://doi.org/10.1134/S2070046621040051
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DOI: https://doi.org/10.1134/S2070046621040051