The Construction of $$p$$-Adic Stockwell Transform and its Spectra$$^*$$

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.