Abstract
In this paper, we extend the one-dimensional Stockwell transform discussed in Stockwell et al. (IEEE Trans Signal Process 44:998-1001, 1996) to the Dunkl theory seeting. We obtain the expected properties of the extended Stockwell transform such as Parseval's formula, inversion formula, Calderon's formula. Next, some applications are given as the uncertainty principles and the theory of localization operators associated with this new transform.