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

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