Bohr-Sommerfeld quantization conditions for non-selfadjoint perturbations of selfadjoint operators in dimension one

Ophélie Rouby

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arXiv · 1511.06237

Bohr-Sommerfeld quantization conditions for non-selfadjoint perturbations of selfadjoint operators in dimension one

Ophélie Rouby

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Abstract

In this paper, we give a description of the spectrum of a class of non-selfadjoint perturbations of selfadjoint operators in dimension one and we show that it is given by Bohr-Sommerfeld quantization conditions. To achieve this, we make use of previous work by Michael Hitrik, Anders Melin and Johannes Sj{\"o}strand. We also give an application of our result in the case of PT-symmetric pseudo-differential operators.

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BibTeX RIS

Ophélie Rouby. 2015-11-19. Bohr-Sommerfeld quantization conditions for non-selfadjoint perturbations of selfadjoint operators in dimension one. https://arxiv.org/abs/1511.06237

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