Boundary Value Problems
Volume 2008 (2008), Article ID 628973, 22 pages
Uniform Convergence of the Spectral
Expansion for a Differential Operator
with Periodic Matrix Coefficients
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.