J-对称微分算子自共轭域的辛几何刻画（Ⅲ）

doi:10.3696/j.issn.1672-6952.2011.04.021

辽宁石油化工大学学报 ›› 2011, Vol. 31 ›› Issue (4): 80-83.DOI: 10.3696/j.issn.1672-6952.2011.04.021

J-对称微分算子自共轭域的辛几何刻画（Ⅲ）

王志敬，李丽君

辽宁石油化工大学理学院，辽宁抚顺 113001

收稿日期:2011-08-30 出版日期:2011-12-25 发布日期:2017-07-14

Symplectic Geometry Characterization of Self-Adjoint DomainsforJ-Symmetric Differential Operators (Ⅲ)

WANG Zhi-jing, LI Li-jun

School of Sciences, Liaoning Shihua University, Fushun Liaoning 113001,P.R.China

Received:2011-08-30 Published:2011-12-25 Online:2017-07-14

摘要/Abstract

摘要： 研究了二阶奇型J-对称微分算子辛几何刻画问题,通过构造商空间，应用辛几何的方法讨论了二阶J-对称微分算子的自共轭扩张问题。给出了与二阶微分算子自共轭域相对应的完全J-Lagrangian子流型的分类与描述。

关键词: 微分算子, J-辛空间, J-Lagrangian子流型

Abstract: The symplectic geometry characterization of second order singular J- symmetric differential operators was investigated. By constructing different quotient spaces, self-adjoint extensions of second order J- symmetric differential operators were studied using the method of symplectic geometry. Then classification and description of complete J-Lagrangian submanifold corresponding with self-adjoint domains of second order differential operators were obtained.

Key words: Differential operators, J-Symplectic spaces, J-Lagrangian submanifold

王志敬，李丽君. J-对称微分算子自共轭域的辛几何刻画（Ⅲ）[J]. 辽宁石油化工大学学报, 2011, 31(4): 80-83.

WANG Zhi-jing, LI Li-jun. Symplectic Geometry Characterization of Self-Adjoint DomainsforJ-Symmetric Differential Operators (Ⅲ)[J]. Journal of Liaoning Petrochemical University, 2011, 31(4): 80-83.

[1]	王志敬. J-对称微分算子自共轭域的辛几何刻画(Ⅱ)[J]. 辽宁石油化工大学学报, 2011, 31(3): 78-80.
[2]	王志敬. 直和空间上对称微分算子自共轭域的辛几何刻画(Ⅵ)[J]. 辽宁石油化工大学学报, 2011, 31(2): 73-76.
[3]	王志敬. 直和空间上对称微分算子自共轭域的辛几何刻画(V)[J]. 辽宁石油化工大学学报, 2011, 31(1): 64-66.
[4]	姜凤利,赵晓颖. J-对称微分算子自共轭域的辛几何刻画(I)[J]. 辽宁石油化工大学学报, 2011, 31(1): 72-75.
[5]	王志敬. 直和空间上对称微分算子自共轭域的辛几何刻画(Ⅳ)[J]. 辽宁石油化工大学学报, 2010, 30(2): 68-70.
[6]	王志敬. 直和空间上对称微分算子自共轭域的辛几何刻画(Ⅲ)[J]. 辽宁石油化工大学学报, 2010, 30(1): 84-87.
[7]	王志敬. 直和空间上对称微分算子自共轭域的辛几何刻画(Ⅱ)[J]. 辽宁石油化工大学学报, 2009, 29(4): 83-86.

J-对称微分算子自共轭域的辛几何刻画（Ⅲ）

Symplectic Geometry Characterization of Self-Adjoint DomainsforJ-Symmetric Differential Operators (Ⅲ)

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