Localization operators, time frequency concentration and quantitative-type uncertainty for the continuous wavelet transform associated with spherical mean operator

摘要

We consider the continuous wavelet transform Φh associated with the spherical mean operator. We investigate the localization operators for Φh, 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 Φh.