Jeffrey Galkowski

A Quantitative Vainberg Method for Black Box Scattering

We give a quantitative version of Vainberg’s method relating pole free regions to propagation of singularities for black box scatterers. In particular, we show that there is a logarithmic resonance free region near the real axis of size

The L2 behavior of eigenfunctions near the glancing set

{\tau}

Distribution of Resonances in Scattering by Thin Barriers

τ with polynomial bounds on the resolvent if and only if the wave propagator gains derivatives at rate

On the growth of eigenfunction averages: microlocalization and geometry

{\tau}

L^\infty

τ. Next we show that if there exist singularities in the wave trace at times tending to infinity which smooth at rate