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

Ophélie Rouby (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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 Sjöstrand. We also give an application of our result in the case of PT-symmetric pseudo-differential operators.

Mots clés: Semi-classical analysis; Spectrum; Non-selfadjoint operators

Domaines: Théorie spectrale [math.SP]; Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Ophélie Rouby. Bohr–Sommerfeld quantization conditions for non-selfadjoint perturbations of selfadjoint operators in dimension one. International Mathematics Research Notices, 2018, 7, pp.2156-2207. ⟨10.1093/imrn/rnw309⟩. ⟨hal-01226209⟩