Isoresonant complex-valued potentials and symmetries

Abstract

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 ${\mathbb{R}}^{+}$. 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.

32 pages

Cited by in corpus (3)

• Resonant rigidity for Schrödinger operators in even dimensions
• Lower bounds for resonance counting functions for Schrödinger operators with fixed sign potentials in even dimensions
• Resonances for Schrödinger operators on infinite cylinders and other products