Uniform convergence of the spectral expansion for a differential operator with periodic matrix coefficients
CitationVELİEV, O. (2008). Uniform convergence of the spectral expansion for a differential operator with periodic matrix coefficients. Boundary Value Problems, pp. 1-22. http://dx.doi.org/ 10.1155/2008/628973.
We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coeffcients and the quasiperiodic boundary conditions. Using these asymptotic formulas, we find conditions on the coeffcients 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 coeffcients.