Speaker
Haruya Mizutani
Description
We will present recent results on uniform weighted resolvent estimates, or equivalently limiting absorption principles with uniform bounds with respect to the spectral parameter, for two non-elliptic differential operators. One is the massless Klein-Gordon operator on the asymptotically Minkowski spacetime with a sufficiently small metric perturbation and the other is the sub-Laplacian on the Heisenberg group. In both cases, the main technical tool is the method of weakly conjugate operators, which is a variant of Mourre’s commutator method, with conjugate operators involving the generator of dilation and some non-local Sobolev weights. This talk is partly based on joint work with Luca Fanelli, Luz Roncal and Nico Michele Schiavone.
