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  • Research Article
  • 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:

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.

Keywords

  • Boundary Condition
  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation

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Authors’ Affiliations

(1)
Departartment of Mathematics, Faculty of Arts and Science, Dogus University, Acibadem, Kadikoy, Istanbul, 34722, Turkey

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