On Spectral Properties of Elliptic Pseudo-Differential Operators Far from Self-Adjoint Ones

Abstract

We establish a rough asymptotics for eigenvalues of elliptic operators under some assumptions; one of them is that the values of the principal symbol do not cover the whole complex plane. We consider also a collection of some examples of non-self-adjoint elliptic operators: in particular, with unusual formulas for asymptotics of eigenvalues; with a regular asymptotics of eigenvalues but without the completeness of root functions; with a complete system of eigenfunctions which is not a basis.