On non-self-adjoint sturm-liouville operators in the space of vector functions

Abstract

In this article we obtain asymptotic formulas for the eigenvalues and eigenfunctions of the non-self-adjoint operator generated in L-2(m) [0, 1] by the Sturm-Liouville equation with m x m matrix potential and the boundary conditions which, in the scalar case (m = 1), are strongly regular. Using these asymptotic formulas, we find a condition on the potential for which the root functions of this operator form a Riesz basis.