Spectral asymptotics for
non-selfadjoint operators in 2 dimensions
(by Johannes Sjöstrand)
Following a work of the speaker with A. Melin, it has
appeared that non-selfadjoint operators in two dimensions share many of
the pleasant feutures of operators in one dimension. It is often possible to
give full asymptotics for all eigenvalues in some fixed domain of the complex
plane, in the semi-classical limit. In this talk we describe some results in this
direction obtained jointly with M. Hitrik, as part of an ongoing program on
small non-selfadjoint perturbations of self-adjoint operators. We also hope
to discuss applications to barrier top resonances and to the damped
wave-equation.