Some Abelian results for the distributional Stockwell transform

Abstract

We give several Abelian results characterizing the quasiasymptotic behavior of distributions at origin (resp. at infinity) in $\mathcal{S}_{0}'(\mathbb{R})$, in terms of their Stockwell transform, using known quasiasymptotic behavior for the polynomial multiplication and $m$-th derivative of a distribution $f \in \mathcal{S}_{0}'(\mathbb{R})$.