三阶奇异微分算子自伴边界条件的标准型
Canonical Forms of Boundary Conditions for Singular Differential Operators of Order Three
摘要:
三阶奇异自伴微分算子自伴域的描述与亏指数之间有着紧密的联系。本文利用亏指数的取值与自伴边界条件系数矩阵的阶数之间的代数关系，得到三阶对称微分算子能实现自伴扩张时的亏指数取值并给出了相应的自伴边界条件的标准型。
Abstract:
There is a close relationship between the characterization of the self-adjoint domain and the defi-ciency index. In this paper, using the algebraic relation between the deficiency index and the order of the coefficient matrix of the self-adjoint boundary conditions, we obtain the value of the defi-ciency index when the third-order symmetric differential operator can realize the self-adjoint ex-pansion and give the corresponding canonical forms of the self-adjoint boundary conditions.
参考文献
|
[1]
|
Zettl, A. (2005) Sturm-Liouville Theory, Providence, Rhode Island. American Mathematics Society, Mathematical Surveys and Monographs.
|
|
[2]
|
Zettl, A. and Sun, J. (2015) Survey Article: Self-Adjoint Ordinary Differential Operators and Their Spectrum. Rocky Mountain Journal of Mathematics, 45, 763-886.
[Google Scholar] [CrossRef]
|
|
[3]
|
曹之江. 常微分算子[M]. 上海: 上海科技出版社, 1987.
|
|
[4]
|
刘景麟. 常微分算子谱论[M]. 北京: 科学出版社, 2009.
|
|
[5]
|
Kong, Q. and Zettl, A. (1996) Dependence of Eigenvalues of Sturm-Liouville Problems on the Boundary. Journal of Differential Equations, 126, 389-407.
[Google Scholar] [CrossRef]
|
|
[6]
|
Kong, Q. and Zettl, A. (1996) Eigenvalues of Regular Sturm-Liouville Problems. Journal of Differential Equations, 131, 1-19.
[Google Scholar] [CrossRef]
|
|
[7]
|
Niu, T., Hao, X., Sun, J. and Li, K. Canonical Forms of Self-Adjoint Boundary Conditions for Differential Operators of Order Three. (Submitted)
|
|
[8]
|
牛天, 郝晓玲, 李昆. 三阶正则微分算子特征值关于问题的依赖性. (已投)
|
|
[9]
|
Hao, X., Zhang, M. and Sun, J. (2017) Characterization of Domains of Self-Adjoint Ordinary Differential Operators of Any Order, Even or Odd. Electronic Journal of Qualitative Theory of Differential Equations, 2017, 1-19.
[Google Scholar] [CrossRef]
|