摘要
本文考虑了二维向量空间中二阶微分算子在两区间上自伴扩张的问题,给出了SturmLiouville(S-T)向量微分算式在两区间上生成最小算子的自伴扩张域的解析描述,其中包括区间端点为正则、一端奇异且为极限圆型、两端奇异且为极限圆型的自伴扩张域的描述.
This paper studies the self-adjoint extension of two-interval Sturm-Liouville vector differential operators,according to a theory of self-adjoint realizations of Sturm-Liouville problems on two intervals in the direct sum of Hilbert spaces associated with these intervals.It gives the analytical characterization of the self-adjoint extension domain of the minimal operator generated by Sturm-Liouville(ST)vector differential equations in two intervals.The characterizations include:the characterization of the self-adjoint extension domain with regular endpoints;the characterization of the self-adjoint extension domain with singularity and limit circle at one end;the characterization of the self-adjoint extension domain with singularity and limit circle at both ends.
作者
高雪
许美珍
GAO Xue;XU Mei-zhen(College of Sciences,Inner Mongolian University of Technology,Hohhot 010051)
出处
《内蒙古工业大学学报(自然科学版)》
2018年第2期81-89,共9页
Journal of Inner Mongolia University of Technology:Natural Science Edition
基金
国家自然科学基金项目(11361039
11661059
11561051)
内蒙古自治区基金项目(2017JQ07)
内蒙古工业大学科研基金项目(ZD201716)
关键词
S-T向量微分算子
两区间
正则点
极限圆型
自伴扩张域
ST vector differential operators
Two intervals
Regular points
I.imit circle
Self adjoint extension domain