Non-propagation for zero order pseudodifferential operators

Abstract

We show phase space localization at suitable energies for zero order pseudodiflcrential operators, implying non-propagation properties for the associated eyolution groups. This extends previous results wh.ich only t¡eated configuration space a-nisotropic behavior The proofs rely on Rieffel's strict deformation quantization of C.-algebras acted by a vector group and on a quasiorbit analysis of some connected locally compact dynamical systems.