On the spectral properties of the operators generated by a system of differential equations

We consider non-self-adjoint operator Lm(Q) generated in Lm2 [0; 1] by the Sturm-Liouville equation with m m matrix potential and the boundary conditions, whose scalar case (m = 1) are strongly regular.First we obtain asymptotic formulas for the eigenvalues and eigenfunctions of Lm(Q) and then find a condition on the potential for which the root functions of the operator form a Riesz basis. We also study the approximation of eigenvalues of Lm(Q) by finite difference method. Key words: Differential operators, matrix potential, Riesz basis, asymptotic formulas, eigenvalues, finite difference method ii