Minimal escape velocities for unitary evolution groups
Starting from a strict Mourre inequality, the minimal escape velocity for a unitary evolution group in a Hilbert space is derived under some minimal conditions. If the self-adjoint generator \(H\) of this evolution is a Schrodinger operator and if the conjugate operator is the generator of dilations, then it follows that \(H\) has very good and easily understandable propagation properties. The striking fact is that no proof of the absence of singularly continuous spectrum of \(H\) is available yet under such weak conditions.
scientific article; zbMATH DE number 2123136