%0 Journal Article
%T Non-selfadjoint perturbations of selfadjoint operators in 2 dimensions I
%A Michael Hitrik
%A Johannes Sjoestrand
%J Mathematics
%D 2003
%I arXiv
%R 10.1007/s00023-004-0160-1
%X 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 $[-1/C, 1/C]+ i\epsilon [F_0-1/C,F_0+1/C]$.
%U http://arxiv.org/abs/math/0302297v1