Perturbations of selfadjoint operators with periodic classical flow

Johannes Sjoestrand

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Perturbations of selfadjoint operators with periodic classical flow

Johannes Sjoestrand

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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 $ε$ of the perturbation satisfies $h^{δ_0} <ε\le ε_0$ for some $δ_0\in ]0,1/2[$ and a sufficiently small $ε_0>0$. We get a complete asymptotic description of all eigenvalues in certain rectangles $[-1/C,1/C]+iε[F_0-1/C,F_0+1/C]$. In particular we are able to treat the case when $ε>0$ is small but independent of $h$.

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BibTeX RIS

Johannes Sjoestrand. 2003-03-03. Perturbations of selfadjoint operators with periodic classical flow. https://arxiv.org/abs/math/0303023

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