New results on the continuous Weinstein wavelet transform

Abstract

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 $\mathcal{S}_{h}^{W}$ .

Keywords

• Weinstein operator
• Weinstein wavelet transform
• localization operators
• Schatten-von Neumann class
• Heisenberg’s type inequalities