On Sharp Asymptotic Formulas for the Sturm-Liouville Operator with a Matrix Potential

摘要

In this article we obtain the sharp asymptotic formulas for the eigenvalues and eigen-functions of the non-self-adjoint operators generated by a system of the Sturm-Liouville equations with Dirichlet and Neumann boundary conditions. Using these asymptotic formulas, we find a condition on the potential for which the root functions of these operators form a Riesz basis.