Essential spectrum of non-self-adjoint singular matrix differential operators.

The purpose of this paper is to study the essential spectrum of non-self-adjoint singular matrix differential operators in the Hilbert space L 2 ( R ) ⊕ L 2 ( R ) induced by matrix differential expressions of the form (0.1) ( τ 11 ( ⋅ , D ) τ 12 ( ⋅ , D ) τ 21 ( ⋅ , D ) τ 22 ( ⋅ , D ) ) , where τ 11 , τ 12 , τ 21 , τ 22 are respectively m -th, n -th, k -th and 0 order ordinary differential expressions with m = n + k being even. Under suitable assumptions on their coefficients, we establish an analytic description of the essential spectrum. It turns out that the points of the essential spectrum either have a local origin, which can be traced to points where the ellipticity in the sense of Douglis and Nirenberg breaks down, or they are caused by singularity at infinity. [ABSTRACT FROM AUTHOR]