On Hill's operator with a matrix potential

Veliev, Oktay A. (Dogus Author)In this article we obtain asymptotic formulas for eigenvalues and eigenfunctions of the self-adjoint operator generated by a system of Sturm-Liouville equations with summable coefficients and quasiperiodic boundary conditions. Then using these asymptotic formulas, we find conditions on the potential for which the number of gaps in the spectrum of the Hill's operator with matrix potential is finite