| Abstract: |
| We will discuss the generic simplicity of the spectrum of self-adjoint
operators under bounded potential perturbations. More precisely, given a
semibounded self-adjoint operator with compact resolvent and a suitable
space of real-valued bounded perturbations, we will analyse whether all eigenvalues
of the perturbed operator are simple for a generic choice of the potential.
We will also discuss several geometric and analytic
settings, including sub-Laplacians and maximally hypoelliptic operators on
compact manifolds, Laplacians on bounded domains with different boundary
conditions, and Schrödinger-type operators on non-compact spaces.\
The talk is based on a joint work with Bernard Helffer. |
|