具有周期复系数的2n阶微分算子的谱

The Spectrum of Differential Operators of 2n-th Order with Periodic Complex Coefficients

本文研究了具有周期复系数的2n阶J-对称微分算子,利用分析和算子理论的方法,得到了这类J-对称微分算子是本质J-自伴微分算子,并给出它的谱为纯连续谱且在复平面上或者是由一些解析弧段构成,或者是整个复平面.

In this paper, we study the J-symmetric differential operators of 2n-th order with periodic complex coefficients. Using the methods of analysis and operator theory, we obtain that the J-symmetric differential operators are essential J-self-adjoint operators in L2（-∞, ＋∞） and only have continuous spectrum. The distribution of their spectrum in the complex plane consist, either of an infinite number of analytic arcs , or fills the whole complex plane.