New results on the continuous Weinstein wavelet transform

• Main Authors: Hatem Mejjaoli, Ahmedou Ould Ahmed Salem
• Format: Article
• Language: English
• Published: SpringerOpen 2017-10-01
• Series: Journal of Inequalities and Applications
• Subjects: Weinstein operator; Weinstein wavelet transform; localization operators; Schatten-von Neumann class; Heisenberg’s type inequalities
• Online Access: http://link.springer.com/article/10.1186/s13660-017-1534-5

Abstract We consider the continuous wavelet transform S h W $\mathcal{S}_{h}^{W}$ associated with the Weinstein operator. We introduce the notion of localization operators for S h W $\mathcal {S}_{h}^{W}$ . In particular, we prove the boundedness and compactness of localization operators associated with the continuous wavelet transform. Next, we analyze the concentration of S h W $\mathcal{S}_{h}^{W}$ on sets of finite measure. In particular, Benedicks-type and Donoho-Stark’s uncertainty principles are given. Finally, we prove many versions of Heisenberg-type uncertainty principles for S h W $\mathcal{S}_{h}^{W}$ .