Fractional Stockwell transform of Lizorkin distributions

Abstract

We prove the continuity of the fractional Stockwell transform and the corresponding synthesis operator on the spaces of highly localized functions over $\mathbb{R}$ and $\mathbb{R}\times \mathbb{R}\setminus \{0\}$, respectively, and their duals. We also provide Abelian and Tauberian-type results relate the asymptotic behaviour of distributions with the asymptotics of their fractional Stockwell transform.

Keywords:

• Fractional Stockwell transform
• distributions
• Abelian and Tauberian theorems

AMS CLASSIFICATIONS:

• 46F10
• 46F12
• 40E05
• 42C40

Disclosure statement

No potential conflict of interest was reported by the author(s).