On the spectral properties of Non- selfadjoint Elliptic Differential Operators in Hilbert space

Abstract

The non-self-adjoint operators appear in many branches of science, from kinetic theory and quantum me-chanics to linearizations of equations of mathematical physics. Non-self-adjoint operators are usually difficultto study because of the lack of general spectral theory. In this paper, our aim is to study the resolvent andthe spectral properties of a class of non-self-adjoint differential operators. .