Abstract
We consider the continuous wavelet transform Phi(h) associated with the spherical mean operator. We investigate the localization operators for Phi(h), in particular, we prove that they are in the Schatten-von Neumann class. Next, we analyze the concentration of this transform on sets of finite measure. In particular, Donoho-Stark and Benedicks-type uncertainty principles are given. Finally, we prove many versions of quantitative uncertainty principles for Phi(h).