Open Access

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

Boundary Value Problems20082008:628973

https://doi.org/10.1155/2008/628973

Received: 6 May 2008

Accepted: 23 July 2008

Published: 29 July 2008

Abstract

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.

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Authors’ Affiliations

(1)
Departartment of Mathematics, Faculty of Arts and Science, Dogus University

Copyright

© O. A. Veliev. 2008

This article is published under license to BioMed Central Ltd. 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.