Symplectic Geometry Characterization of Self-Adjoint Domains for Symmetric Differential Operators in Direct Sum Spaces(Ⅳ)

doi:10.3696/j.issn.1672-6952.2010.02.019

Journal of Liaoning Petrochemical University ›› 2010, Vol. 30 ›› Issue (2): 68-70.DOI: 10.3696/j.issn.1672-6952.2010.02.019

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Symplectic Geometry Characterization of Self-Adjoint Domains for Symmetric Differential Operators in Direct Sum Spaces(Ⅳ)

WNAG Zhi-jing

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

Received:2008-10-25 Published:2010-06-25 Online:2017-07-05

直和空间上对称微分算子自共轭域的辛几何刻画(Ⅳ)

王志敬

辽宁石油化工大学理学院,辽宁抚顺113001

作者简介:王志敬(1975-),男,河南枣强县,硕士。
基金资助:
辽宁省教育厅高校科研项目(2004F100);辽宁石油化工大学重点学科建设项目(K200409)。

Abstract

Abstract:

The characterization of self-adjoint domains for symmetric differential operators with interior singular points in the direct sum spaces was investigated. By constructing different quotient spaces, using the method of symplectic geometry, the self-adjoint extensions of symmetric differential operators in the direct sum spaces for the different deficiency indices at middle deficiency indices singular points were studied. The classification and description of complete Lagrangian subman-ifold that correspond with self-adjoint domains of second order differential operators were given.

Key words: Differential operators , Symplectic spaces , Lagrangian submanifold , Singular points , Direct sum spaces

摘要： 研究了具有内部奇异点,即直和空间上的高阶对称微分算子辛几何刻画问题。由于对称微分算子在
端点处的亏指数取值情况不同,当微分算子在端点处取中间亏指数时,通过构造商空间,应用辛几何的方法讨论了
直和空间的对称微分算子的自共轭扩张问题。给出了与高阶微分算子自共轭域相对应的完全Lagrangian子流型的
分类与描述。

关键词: 微分算子 , 辛空间 , Lagrangian子流型 , , 奇异点 , 直和空间

WNAG Zhi-jing.

Symplectic Geometry Characterization of Self-Adjoint Domains for Symmetric Differential Operators in Direct Sum Spaces(Ⅳ)

[J]. Journal of Liaoning Petrochemical University, 2010, 30(2): 68-70.

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.

[1]	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.
[2]	WANG Zhi-jing. Symplectic Geometry Characterization of Self-Adjoint Domainsfor J-Symmetric Differential Operators (Ⅱ) [J]. Journal of Liaoning Petrochemical University, 2011, 31(3): 78-80.
[3]	WANG Zhi-jing. Symplectic Geometry Characterization of Self-Adjoint Domains for Symmetric Differential Operators in Direct Sum Spaces(VI) [J]. Journal of Liaoning Petrochemical University, 2011, 31(2): 73-76.
[4]	WANG Zhi-jing. Symplectic Geometry Characterization of Self-Adjoint Domains for Symmetric Differential Operators in Direct Sum Spaces(V) [J]. Journal of Liaoning Petrochemical University, 2011, 31(1): 64-66.
[5]	JIANG Feng-li, ZHAO Xiao-ying. Symplectic Geometry Characterization of Self-Adjoint Domainsfor J-Symmetric Differential Operators (I) [J]. Journal of Liaoning Petrochemical University, 2011, 31(1): 72-75.
[6]	WANG Zhi-jing. Symplectic Geometry Characterization of Self-Adjoint Domains for Symmetric Differential Operators in Direct Sum Spaces(Ⅲ) [J]. Journal of Liaoning Petrochemical University, 2010, 30(1): 84-87.
[7]	WANG Zhi-jing. Symplectic Geometry Characterization of Self-Adjoint Domains for Symmetric Differential Operators in Direct Sum Spaces（Ⅱ） [J]. Journal of Liaoning Petrochemical University, 2009, 29(4): 83-86.

Symplectic Geometry Characterization of Self-Adjoint Domains for Symmetric Differential Operators in Direct Sum Spaces(Ⅳ)

直和空间上对称微分算子自共轭域的辛几何刻画(Ⅳ)

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