Let $X$ be a connected Riemannian manifold such that the resolvent of the free Laplacian $(\Delta-z)^{ -1}, z\in\C\setminus\R^{ +},$ has a meromorphic continuation through $\R^{ +}$. The poles of this continuation are called resonances. When $X$ has some symmetries, we construct complex-valued potentials, $V$, such that the resolvent of $\Delta+V$, which has also a meromorphic continuation, has the same resonances with multiplicities as the free Laplacian.
Categories: math.SP