Abelian and Tauberian results for the one-dimensional modified Stockwell transforms

The aim of this paper is to study the asymptotic behavior of one- dimensional modified Stockwell transform of a tempered distribution signal through the quasiasymptotic behavior at origin or infinity of the signal itself. More precisely, we give some Abelian results which mean that we derive the asymptotic properties of the S-transform of a tempered signal from the quasiasymptotic properties of the signal itself and we do also the opposite. So, we also give some Tauberian results which describe some quasiasymptotic properties of the tempered signal by means of the asymptotic properties of its Stockwell transform.