Several complex variables and the distribution of resonances in potential scattering

Abstract

We study resonances associated to Schrödinger operators with compactly supported potentials on ${\mathbb{R}}^d$, $d\ge 3$, odd. We consider compactly supported potentials depending holomorphically on a complex parameter $z$. For certain such families, for all $z$ except those in a pluripolar set, the associated resonance-counting function has order of growth $d$. Our proofs use some results from several complex variables.

18 pages