Jun 24 – 28, 2024
Institut de Mathématiques de Toulouse
Europe/Paris timezone

Uniform resolvent estimates for a few non-elliptic operators

Jun 25, 2024, 2:30 PM
Institut de Mathématiques de Toulouse

Institut de Mathématiques de Toulouse

Université Paul Sabatier 118, route de Narbonne - Bat. 1R3 31062 Toulouse Cedex 9


Haruya Mizutani


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.

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