Bohr-Sommerfeld quantization condition for non-selfadjoint operators in dimension 2

A. Melin; J. Sjoestrand

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arXiv · math/0111293

Bohr-Sommerfeld quantization condition for non-selfadjoint operators in dimension 2

A. Melin·J. Sjoestrand

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Abstract

For a class of non-selfadjoint h-pseudodifferential operators in dimension 2, we determine all eigenvalues in an h-independent domain in the complex plane and show that they are given by a Bohr-Sommerfeld quantization condition. No complete integrability is assumed, and as a geometrical step in our proof, we get a KAM-type theorem (without small divisors) in the complex domain.

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BibTeX RIS

A. Melin, J. Sjoestrand. 2001-11-28. Bohr-Sommerfeld quantization condition for non-selfadjoint operators in dimension 2. https://arxiv.org/abs/math/0111293

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