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

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

2001-11-28

arxiv.org/abs/math/0111293v1

Mathematics

Spectral Theory

Scientific paper

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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