两区间二维Sturm-Liouville向量微分算子的自伴扩张  

Self-adjoint Expansion of Two-Dimensional Sturm-Liouville Vector Differential Operators in Two-interval

作　　者：高雪 许美珍[1] GAO Xue;XU Mei-zhen(College of Sciences,Inner Mongolian University of Technology,Hohhot 010051)

机构地区：[1]内蒙古工业大学理学院

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)

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.

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 

分 类 号：O175.3[理学—数学]