2000 character limit reached
Diophantine tori and Weyl laws for non-selfadjoint operators in dimension two (1102.0889v1)
Published 4 Feb 2011 in math.SP and math.AP
Abstract: We study the distribution of eigenvalues for non-selfadjoint perturbations of selfadjoint semiclassical analytic pseudodifferential operators in dimension two, assuming that the classical flow of the unperturbed part is completely integrable. An asymptotic formula of Weyl type for the number of eigenvalues in a spectral band, bounded from above and from below by levels corresponding to Diophantine invariant Lagrangian tori, is established. The Weyl law is given in terms of the long time averages of the leading non-selfadjoint perturbation along the classical flow of the unperturbed part.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.