Michael Hitrik, UCLA, Spectra for non-selfadjoint operators in two dimensions

Abstract: We study the distribution of eigenvalues of non-selfadjoint perturbations of semiclassical selfadjoint operators, with a completely integrable classical flow. In an earlier work with Johannes Sjöstrand and San Vu Ngoc, we have analyzed the eigenvalues with imaginary parts close to certain levels corresponding to suitable Diophantine tori of the classical system. Here I would like to describe an asymptotic formula, of Weyl type, for the number of eigenvalues in a spectral band, bounded from above and from below by such Diophantine levels. This is joint work with J. Sjöstrand.