This is the first in a series of works devoted to small non-selfadjoint
perturbations of selfadjoint $h$-pseudodifferential operators in dimension 2.
In the present work we treat the case when the classical flow of the
unperturbed part is periodic and the strength $\epsilon$ of the perturbation is
$\gg h$ (or sometimes only $\gg h^2$) and bounded from above by $h^{\delta}$
for some $\delta>0$. We get a complete asymptotic description of all
eigenvalues in certain rectangles $[-1/C, 1/C]+ i\epsilon [F_0-1/C,F_0+1/C]$.
@article{0302297,
author = {Hitrik, Michael and Sjoestrand, Johannes},
title = {Non-selfadjoint perturbations of selfadjoint operators in 2 dimensions I},
journal = {arXiv},
volume = {2003},
number = {0},
year = {2003},
language = {en},
url = {http://dml.mathdoc.fr/item/0302297}
}
Hitrik, Michael; Sjoestrand, Johannes. Non-selfadjoint perturbations of selfadjoint operators in 2 dimensions I. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0302297/