Perturbations of selfadjoint operators with periodic classical flow

Abstract

We consider non-selfadjoint perturbations of a self-adjoint $h$-pseudodifferential operator in dimension 2. In the present work we treat the case when the classical flow of the unperturbed part is periodic and the strength $\epsilon$ of the perturbation satisfies $h^{{\delta }_0}<\epsilon \le {\epsilon }_0$ for some ${\delta }_0\in ]0,1/2[$ and a sufficiently small ${\epsilon }_0>0$. We get a complete asymptotic description of all eigenvalues in certain rectangles $[-1/C,1/C]+i\epsilon [F_0-1/C,F_0+1/C]$. In particular we are able to treat the case when $\epsilon >0$ is small but independent of $h$.

Cited by in corpus (2)

• Non-selfadjoint perturbations of selfadjoint operators in 2 dimensions IIIa. One branching point
• Diophantine tori and spectral asymptotics for non-selfadjoint operators