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

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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Correspondence to OA Veliev.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Veliev, O. Uniform Convergence of the Spectral Expansion for a Differential Operator with Periodic Matrix Coefficients. Bound Value Probl 2008, 628973 (2008). https://doi.org/10.1155/2008/628973

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Keywords

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