Luca Fanelli: A priori estimates for the resolvent of the Heisenberg sublaplacian

Speaker

Luca Fanelli, University of the Basque Country

Abstract
he sub-laplacian on the Heisenberg Group $\mathbb H^d$ is a standard example of sub-elliptic operator in a sub-Riemannian geometry. In this talk, we will first introduce some natural inequalities related to the Uncertainty Principle (Hardy, Rellich), then study some recent uniform versions of the same inequalities for the resolvent operator, over the complex plane. As an application, we obtain local smoothing estimates for the associated Schrödinger evolution flow, which is known to show a lack of the usual dispersion, due to the presence of soliton-like solutions.
The results are obtained in collaboration with H. Mizutani (Osaka University), L. Roncal and N. Schiavone (BCAM – Bilbao).