"Recent results on the norm of localization operators"Riccardi, FedericoIn this talk we will present some new estimates for the norm of time-frequency localization operators with Gaussian window in the spirit of Lieb's uncertainty inequality. We provide some optimal estimates under the assumption that the weight function belongs to the intersection of two Lebesgue spaces and we also provide a full characterization of the extremizers. We conclude with an estimate for the Hilbert-Schmidt norm of these operators with a corresponding stability result in the case where the weight function is a characteristic function. In particular, we show how the latter issue is intimately connected with some rearrangement and energy inequalities recently proved by M. Christ, R. Frank and E. H. Lieb. We will also discuss some conjectures in this connection. This is a joint work with Fabio Nicola (Politecnico di Torino). |
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