%0 Journal Article
%T Schr£żdinger operators with complex-valued potentials and no resonances
%A T. Christiansen
%J Mathematics
%D 2004
%I arXiv
%X In dimension $d\geq 3$, we give examples of nontrivial, compactly supported, complex-valued potentials such that the associated Schr\"odinger operators have no resonances. If $d=2$, we show that there are potentials with no resonances away from the origin. These Schr\"odinger operators are isophasal and have the same scattering phase as the Laplacian on $\Real^d$. In odd dimensions $d\geq 3$ we study the fundamental solution of the wave equation perturbed by such a potential. If the space variables are held fixed, it is super-exponentially decaying in time.
%U http://arxiv.org/abs/math-ph/0408052v1