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.

中文翻译：

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$$p$$ -Adic Wiener Tauberian 定理的分布证明和通过函数平移的近似

摘要

使用\(p\) -adic 分布，我们获得了卷积的唯一性结果。作为这一结果的推论，可以得到\(p\) -adic Wiener Tauberian 定理和 Wiener 近似定理。我们还证明了\(L^1(\mathbb Q^n_p)\) 没有由函数的平移组成的基。