周期矩阵系数微分算子谱展开的一致收敛性
Uniform Convergence of the Spectral Expansion for a Differential Operator with Periodic Matrix Coefficients
摘要：
本文给出了一类具有可和系数的常微分方程在拟周期边界条件下生成的算子的本征值和本征函数的渐近公式。使用这些渐近公式，我们找到的条件，该运营商的根函数的系数形成一个Riesz基础。然后得到了具有周期矩阵系数的微分算子的一致收敛谱展开式
英文摘要：
In this paper, 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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