Speaker: Xianchao Wu (McGill University)
Title: Reverse Agmon Estimate and some applications
Abstract: We consider L^2-normalized eigenfunctions of the semiclassical Schrodinger operator on a compact manifold. The well-known Agmon-Lithner estimates are exponential decay estimates (ie. upper bounds) for eigenfunctions in the forbidden region. The decay rate is given in terms of the Agmon distance function which is associated with the degenerate Agmon metric with support in the forbidden region.
The point of this talk is to prove a partial converse to the Agmon estimates (ie. exponential lower bounds for the eigenfunctions) in terms of Agmon distance in the forbidden region under a control assumption on eigenfunction mass in the allowable region arbitrarily close to its boundary. And some improvement estimates in the analytic setting will also be considered.
We then give some applications to hypersurface restriction bounds for eigenfunctions in the forbidden region along with corresponding nodal intersection estimates.