On the trace of the wave group and regularity of potentials

Abstract

For the wave equation ${\partial }_t^2-\Delta +V$ on ${\mathbb{R}}^d$ with compactly supported, real valued potential $V$, we establish a sharp relation between Sobolev regularity of $V$ and the existence of finite order expansions as $t\to 0$ for the relative trace of the wave group.

arXiv comment31 pages