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

doi:10.3696/j.issn.1672-6952.2011.02.019

Journal of Liaoning Petrochemical University ›› 2011, Vol. 31 ›› Issue (2): 73-76.DOI: 10.3696/j.issn.1672-6952.2011.02.019

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

WANG Zhi-jing

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

Received:2010-04-06 Published:2011-06-25 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(Ⅵ)

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资助项目(K200409)

Abstract

Abstract:

Interior singular points were mainly studied in this paper,which means the characterization of self-adjoint domains for symmetric differential operators in the direct sum spaces. There exist the different deficiency indices at (n,n)singular points.Therefore by constructing different quotient spaces and using the method of symplectic geometry, it is possible to study self-adjoint extensions of symmetric differential operators in the direct sum spaces.The classification and description of complete Lagrangian submanifold that corresponds with self-adjoint domains of second order differential operators were also produced .

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均取(n,n)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。给出了与二阶对称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

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.

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.

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

直和空间上对称微分算子自共轭域的辛几何刻画(Ⅵ)

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