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, Calderón’s formula. Next, some applications are given as the uncertainty principles and the theory of localization operators associated with this new transform.

中文翻译：

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Dunkl–Stockwell变换及其在时频分析中的应用

在本文中，我们扩展了Stockwell等人中讨论的一维Stockwell变换。（IEEE Trans Signal Process 44：998–1001，1996）符合Dunkl理论。我们获得扩展的Stockwell变换的预期属性，例如Parseval公式，反演公式，Calderón公式。接下来，给出了一些应用程序，如不确定性原理和与此新变换相关联的定位算符理论。