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

作　　者：王文娟[1] 王忠[2] 

机构地区：[1]内蒙古工业大学理学院,呼和浩特010051 [2]肇庆学院数学与统计学院,肇庆526061

出　　处：《应用数学学报》2015年第4期699-707,共9页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11171295)资助项目

摘　　要：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.

关 键 词：周期复系数 J-自伴算子 点谱 连续谱 解析弧段 

分 类 号：O175.3[理学—数学]