Time-frequency analysis associated with the generalized Stockwell transform

The Riemann-Liouville operator has been extensively investigated and has witnessed a remarkable development in numerous fields of harmonic analysis. In this paper, we consider the Stockwell transform associated with the Riemann-Liouville operator. Knowing the fact that the study of the time-frequency analysis are both theoretically interesting and practically useful, we investigated several problems for this subject on the setting of this generalized Stockwell transform. Firstly, we study the boundedness and compactness of localization operators associated with the generalized Stockwell transform. Next, we explore the Shapiro uncertainty principle for the previous transform. Finally, the scalogram for the generalized Stockwell transform are introduced and studied at the end.