Uniform Convergence of the Spectral Expansion for a Differential Operator with Periodic Matrix Coefficients

Abstract

In this paper, we obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and the quasiperiodic boundary conditions. Using these asymptotic formulas, we find conditions on the coefficients for which the root functions of this operator form a Riesz basis. Then we obtain the uniformly convergent spectral expansion of the differential operators with the periodic matrix coefficient