Semi-classical dispersive estimates

TL;DR

This paper establishes dispersive estimates for wave and Schrödinger groups linked to elliptic operators with a semi-classical parameter, with applications to metric and magnetic perturbations.

Contribution

It provides new dispersive estimates for elliptic operators under semi-classical regimes, extending previous results to include magnetic and metric perturbations.

Findings

Dispersive estimates are proven for wave and Schrödinger groups.

Results apply to non-trapping metric perturbations.

Extensions include magnetic potential perturbations.

Abstract

We prove dispersive estimates for the wave and Schrodinger groups associated to a second-order elliptic self-adjoint operator depending on a semi-classical parameter. Applications are made to non-trapping metric perturbations and to perturbations by a magnetic potential.