一类内部具有无穷多个不连续点Sturm-Liouville算子的亏指数

数学物理学报 ›› 2018, Vol. 38 ›› Issue (3): 484-495.

一类内部具有无穷多个不连续点Sturm-Liouville算子的亏指数

赵迎春^1,2, 孙炯²

1 内蒙古大学数学科学学院呼和浩特 010021;
2 赤峰学院数学与统计学院内蒙古赤峰 024000

收稿日期:2017-02-11 修回日期:2017-10-30 出版日期:2018-06-26 发布日期:2018-06-26
通讯作者: 赵迎春 E-mail:Yingchun_1983@126.com
作者简介:孙炯,E-mail:masun@imu.edu.cn
基金资助:
国家自然科学基金（11561050，11702038）

The Deficiency Index of a Class of Sturm-Liouville Operators with an Infinite Number of Interior Discontinuous Points

Zhao Yingchun^1,2, Sun Jiong²

1 School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021;
2 School of Mathematics and Statistics, Chi Feng University, Inner Mongolia Chifeng 024000

Received:2017-02-11 Revised:2017-10-30 Online:2018-06-26 Published:2018-06-26
Supported by:
Supported by the NSFC (11561050, 11702038)

摘要/Abstract

摘要： 该文研究了一类内部具有无穷多个不连续点SturmLiouville问题.首先，构造了新的Hilbert空间，并其上定义了与不连续条件有关的最小算子和最大算子.进一步地，在新空间框架下，讨论了与不连续条件相关联的最小算子亏指数.

关键词: Sturm-Liouville算子, 不连续性, 不连续条件, 亏指数

Abstract: In this paper, we study a class of Sturm-Liouville problems with an infinite number of interior discontinuous points, i.e., Sturm-Liouville problems with an infinite number of discontinuous conditions at interior points. Firstly, we construct a new Hilbert space associated with the discontinuous conditions and define the maximal and minimal operators associated with the discontinuous conditions in the new Hilbert space. And then we discuss the deficiency index of the minimal operator associated with the discontinuous conditions in the new Hilbert space.

Key words: Sturm-Liouville operator, Discontinuity, Discontinuous condition, Deficiency index

中图分类号:

O175.1

赵迎春, 孙炯. 一类内部具有无穷多个不连续点Sturm-Liouville算子的亏指数[J]. 数学物理学报, 2018, 38(3): 484-495.

Zhao Yingchun, Sun Jiong. The Deficiency Index of a Class of Sturm-Liouville Operators with an Infinite Number of Interior Discontinuous Points[J]. Acta mathematica scientia,Series A, 2018, 38(3): 484-495.

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