Isoresonant complex-valued potentials and symmetries
Let $X$ be a connected Riemannian manifold such that the resolvent of the free Laplacian $(Δ-z)^{-1}, z\in\C\setminus\R^{+},$ 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 $Δ+V$, which has also a meromorphic continuation, has the same resonances with multiplicities as the free Laplacian.
math.SP↗