Asymptotic Relations for the Distributional Stockwell and Wavelet Transforms

Abstract

Abelian- and Tauberian-type results characterizing the quasiasymptotic behavior of distributions in \(\mathcal{S}_{0}'(\mathbb{R})\) in terms of their Stockwell transforms are obtained. An Abelian-type result relating the quasiasymptotic boundedness of Lizorkin distributions to the asymptotic behavior of their Stockwell transforms is given. Several asymptotic results for the distributional wavelet transform are also presented.