The Symplectic Geometry Characterization of Self-Adjoint Domains for Symmetric Differential Operators in Direct SumSpaces（I）

Journal of Petrochemical Universities ›› 2008, Vol. 21 ›› Issue (1): 92-95.

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The Symplectic Geometry Characterization of Self-Adjoint Domains for Symmetric Differential Operators in Direct SumSpaces（I）

WANG Zhi-jing, SONG Dai-cai

School of Sciences, Liaoning University of Petroleum & Chemical Technology, Fushun Liaoning 113001,P.R.China

Received:2007-07-05 Published:2008-03-20 Online:2017-06-28

直和空间上对称微分算子自共轭域的辛几何刻画(I)

王志敬, 宋岱才

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,河北枣强县,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:

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 (2,2)singular points was discussed . The classification and description of complete Lagrangian submanifold that correspond with self-adjoint domains of second order differential operators were given. 

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

摘要： 研究了直和空间上的二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的亏指数均取(2,2)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,并给出了与二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

WANG Zhi-jing, SONG Dai-cai. The Symplectic Geometry Characterization of Self-Adjoint Domains for Symmetric Differential Operators in Direct SumSpaces（I）[J]. Journal of Petrochemical Universities, 2008, 21(1): 92-95.

王志敬, 宋岱才. 直和空间上对称微分算子自共轭域的辛几何刻画(I)[J]. 石油化工高等学校学报, 2008, 21(1): 92-95.

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The Symplectic Geometry Characterization of Self-Adjoint Domains for Symmetric Differential Operators in Direct SumSpaces（I）

直和空间上对称微分算子自共轭域的辛几何刻画(I)

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