On the Nonself-adjoint Sturm-Liouville Operator with Matrix Potential

Abstract

In this article we obtain the asymptotic formulas for the eigenvalues and eigenfunctions of the nonself-adjoint operator generated by a system of Sturm-Liouville equations with summable coefficients and the quasiperiodic boundary conditions. Then using these asymptotic formulas, we find the conditions on the potential for which the root funcions of this operator form a Riesz basis.