Isoresonant complex-valued potentials and symmetries

Aymeric Autin (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

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.

Mots clés: Resonance; symmetries; Laplacian

Domaines: Théorie spectrale [math.SP]

Aymeric Autin. Isoresonant complex-valued potentials and symmetries. Canadian Journal of Mathematics, 2011, 63 (4), pp.721-754. ⟨hal-00380465⟩