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

doi:10.3696/j.issn.1672-6952.2011.01.020

Journal of Liaoning Petrochemical University ›› 2011, Vol. 31 ›› Issue (1): 72-75.DOI: 10.3696/j.issn.1672-6952.2011.01.020

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

JIANG Feng-li, ZHAO Xiao-ying

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

Received:2010-11-29 Published:2011-03-25 Online:2017-07-05

J-对称微分算子自共轭域的辛几何刻画(I)

姜凤利,赵晓颖

辽宁石油化工大学理学院,辽宁抚顺113001

作者简介:姜凤利(1980-),男,辽宁大连市,讲师,硕士。

Abstract

Abstract:

The characterization of self-adjoint domains for symmetric differential operators 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 studied. The classification and description of complete J- Lagrangian submanifold that correspond with self-adjoint domains of second order differential operators were given.

Key words: Differential operators , , J-symplectic spaces , , J-Lagrangian submanifold

摘要： 研究了二阶J-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,当微分算子在端点取(2,2)时,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

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.

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.

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

J-对称微分算子自共轭域的辛几何刻画(I)

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