Uniform Convergence of the Spectral Expansion for a Differential Operator with Periodic Matrix Coefficients
Boundary Value Problems volume 2008, Article number: 628973 (2008)
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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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