二项自伴向量微分算子的本质谱  

Essential Spectrum of the Two-term Self-adjoint Vector Differential Operators

作　　者：钱志祥 林秋红 李小琴[2] QIAN Zhi-xiang;LIN Qiu-hong;LI Xiao-qin(The Department of Basic Education,Guangdong Polytechnic College,Zhaoqing 526100,China;College of General Education,Guangdong University of Science and Technology,Dongguan 523083,China)

机构地区：[1]广东理工学院基础课教学部,广东肇庆526100 [2]广东科技学院通识教育学院,广东东莞523083

出　　处：《数学的实践与认识》2022年第5期179-189,共11页Mathematics in Practice and Theory

基　　金：2019年广东省教育厅自然基金项目(2019KTSCX248);2021年广东省教育厅自然基金项目(2021KTSCX157);2019年广东科技学院科研项目(GKY-2019KYYB-23)。

摘　　要：首先利用算子比较的方法,研究了二项自伴向量微分算子的本质谱,得到了这类微分算子的本质谱分布范围;然后利用算子分解定理,得到了这类算子谱的离散性的一个充分条件;最后得到了Sturm-Liouville算子和Schr?dinger算子的本质谱范围,以及这两类算子谱的离散性的一个充分条件.Firstly using the method of operator comparison,the essential spectrum of higher order self-adjoint,two-term vector differential operators is studied,and the distribution range of essential spectrum of this kind of differential operators is obtained;Then,by using the operator decomposition theorem,a sufficient condition for the discreteness of the spectrum of this kind of operator is obtained;Finally,we obtain the essential spectrum range of SturmLiouville operator and Schrodinger operator,and a sufficient conditions for the discreteness of the spectrum of these two kinds of operators.

关 键 词：自伴向量微分算子 算子比较法 算子分解定理 自伴扩张 本质谱 

分 类 号：O175.3[理学—数学]