Abstract

In this paper, we shall construct the Stockwell transform for complex valued functions in \( {\mathbb{Q}_p} \) and study its properties. Especially, the Stockwell transform of the step function is a function of norms. Moreover, by taking the average of \(p\)-adic parameter of image of Stockwell transform, we give the Stockwell spectra.

中文翻译：

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$$ p $$ -Adic Stockwell变换的构造及其频谱$$ ^ * $$

摘要

在本文中，我们将为\（{\ mathbb {Q} _p} \）中的复数值函数构造Stockwell变换，并研究其性质。特别地，阶跃函数的斯托克韦尔变换是范数的函数。此外，通过取Stockwell变换图像的\（p \）- adic参数的平均值，可以得出Stockwell光谱。