Bohr-Sommerfeld quantization condition for non-selfadjoint operators in dimension 2
谱理论
2007-05-23 v1 数学物理
math.MP
摘要
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.
引用
@article{arxiv.math/0111293,
title = {Bohr-Sommerfeld quantization condition for non-selfadjoint operators in dimension 2},
author = {A. Melin and J. Sjoestrand},
journal= {arXiv preprint arXiv:math/0111293},
year = {2007}
}