Propagation estimates in the one-commutator theory
Sylvain Golenia(Universite de Bordeaux)
Torsdag 17. maj 2018
16:15–17:00Aud. D3 (1531-215)
In the abstract framework of Mourre theory, the propagation of states is understood in terms of a conjugate operator $A$. A powerful estimate has long been known for Hamiltonians $H$ having a good regularity with respect to $A$ thanks to the limiting absorption principle (LAP). We study the case where $H$ has less regularity with respect to $A$, specifically in a situation where the LAP and the absence of singularly continuous spectrum have not yet been established. We show that in this case the spectral measure of $H$ is a Rajchman measure and we derive some propagation estimates.