Abstract view
Isoresonant Complexvalued Potentials and Symmetries


Published:20110525
Printed: Aug 2011
Aymeric Autin,
11 rue Hélène Boucher, 85400 Luçon, France
Abstract
Let $X$ be a connected Riemannian manifold such that the resolvent of
the free Laplacian $(\Deltaz)^{1}$, $z\in\mathbb{C} \setminus
\mathbb{R}^+$, has a meromorphic continuation
through $\mathbb{R}^+$. The poles of this continuation are called
resonances. When $X$ has some symmetries, we construct complexvalued
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.