论文标题
在带有周期性矩阵系数的自动伴侣差分运算符上
On the self-adjoint differential operator with the periodic matrix coefficients
论文作者
论文摘要
在本文中，我们考虑了由M周期矩阵系数与M与M的差异表达一起产生的自相关差异操作器的频谱，其中N和M分别是奇数，甚至整数和N> 1。我们证明，L频谱中的间隙数是有限的，并且在间隙数的系数方面找到了明确的估计。此外，我们找到了有关频谱为真实轴的系数规范的条件。此外，我们研究了频谱的频带，并证明大多数真实轴被M带重叠。
In this paper we consider the spectrum of the self-adjoint differential operator L generated by the differential expression of order n with the m by m periodic matrix coefficients, where n and m are respectively odd and even integers and n>1. We prove that the number of gaps in the spectrum of L is finite and find explicit estimation in term of coefficients for the number of the gaps. Moreover, we find a condition on the norms of the coefficients for which the spectrum is real axis. Besides we investigate the bands of the spectrum and prove that most of the real axis is overlapped by m bands.
