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

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 f...

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Main Author:	O. A. Veliev
Format:	Article
Language:	English
Published:	SpringerOpen 2008-09-01
Series:	Boundary Value Problems
Online Access:	http://dx.doi.org/10.1155/2008/628973

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spelling	doaj-ce53eb3a07d14ba0b4e42b108593165e2020-11-25T00:23:56ZengSpringerOpenBoundary Value Problems1687-27621687-27702008-09-01200810.1155/2008/628973Uniform Convergence of the Spectral Expansion for a Differential Operator with Periodic Matrix CoefficientsO. A. VelievWe 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.http://dx.doi.org/10.1155/2008/628973
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	O. A. Veliev
spellingShingle	O. A. Veliev Uniform Convergence of the Spectral Expansion for a Differential Operator with Periodic Matrix Coefficients Boundary Value Problems
author_facet	O. A. Veliev
author_sort	O. A. Veliev
title	Uniform Convergence of the Spectral Expansion for a Differential Operator with Periodic Matrix Coefficients
title_short	Uniform Convergence of the Spectral Expansion for a Differential Operator with Periodic Matrix Coefficients
title_full	Uniform Convergence of the Spectral Expansion for a Differential Operator with Periodic Matrix Coefficients
title_fullStr	Uniform Convergence of the Spectral Expansion for a Differential Operator with Periodic Matrix Coefficients
title_full_unstemmed	Uniform Convergence of the Spectral Expansion for a Differential Operator with Periodic Matrix Coefficients
title_sort	uniform convergence of the spectral expansion for a differential operator with periodic matrix coefficients
publisher	SpringerOpen
series	Boundary Value Problems
issn	1687-2762 1687-2770
publishDate	2008-09-01
description	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.
url	http://dx.doi.org/10.1155/2008/628973
work_keys_str_mv	AT oaveliev uniformconvergenceofthespectralexpansionforadifferentialoperatorwithperiodicmatrixcoefficients
_version_	1725354935341547520

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

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