Affiliation:
1. Faculté des Sciences de Tunis
2. College of Sciences, 30002 Al Madinah AL Munawarah, Saudi Arabia.
Abstract
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 explore the Shapiro uncertainty principle for this transform. Next, we study the boundedness and compactness of localization operators associated with the generalized Stockwell transforms.
Finally, the scalogram for the generalized Stockwell transform are introduced and studied at the end.
Subject
Geometry and Topology,Statistics and Probability,Algebra and Number Theory,Analysis
Reference31 articles.
1. \bibitem{A-G-R}
{ L. D. Abreu, K. Grochenig and J.L. Romero,} On accumulated
spectrograms, Trans. Amer. Math. Soc. {{368}} (2016) 3629--3649.
2. \bibitem{AWC}
{ P. S. Addison, J.N. Watson, G.R. Clegg, P.A. Steen, C.E. Robertson,} Finding coordinated atrial activity during ventricular fibrilation using wavelt decomposition, analyzing surface ECGs with a new analysis technique to better understand cardiac death, IEEE Trans. Eng. Med. Biol.
{{21}} (2002) 58--65.
3. \bibitem{amri2013beckner}
B. Amri, L. T. Rachdi,
\newblock Beckner logarithmic uncertainty principle for the
{R}iemann-{L}iouville operator,
\newblock {\it Internat. J. Math.} Article ID 1350070, {24}(9) (2013) 1-29.
4. \bibitem{BHR} { C. Baccar, N. B. Hamadi, L. T. Rachdi}, {\em Inversion formulas for the Riemann-Liouville transform and its dual associated with singular partial differential operators,} Int. J. Math. Math.
Sci., Article ID 86238, 2006 (2006), 1-26.
5. \bibitem{Baccar/rachdi/2009}
C. Baccar, L. T. Rachdi,
\newblock Spaces of {DL}p-type and a convolution product associated with the
{R}iemann-{L}iouville operator,
\newblock {\it Bull. Math. Anal. Appl.} {1}(3) (2009), 16--41.