On conditions for the discreteness of the spectrum of a non-self-adjoint system of differential equations of the Dirac type

A first-order non-self-adjoint system of differential equations with 2n unknown functions and with certain conditions on the coefficients is considered on the entire axis. The system is similar to the well-known Dirac system. An operator , associated with the considered system, is introduced in the space L²(– , ) of 2n-component vector-valued functions. Conditions for the compactness of the resolvent of the operator are found, yielding sufficient conditions for the discreteness of its spectrum.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 16, pp. 3–24, 1992.