Boundary Value Problems
Volume 2008 (2008), Article ID 628973, 22 pages
Research Article

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

O. A. Veliev

Departartment of Mathematics, Faculty of Arts and Science, Dogus University, Acibadem, Kadikoy, 34722 Istanbul, Turkey

Received 6 May 2008; Accepted 23 July 2008

Academic Editor: Ugur Abdulla

Copyright © 2008 O. A. Veliev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 coefficients.