直和空间上对称微分算子自共轭域的辛几何刻画(Ⅵ)  

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

作　　者：王志敬[1] 

机构地区：[1]辽宁石油化工大学理学院,辽宁抚顺113001

出　　处：《辽宁石油化工大学学报》2011年第2期73-76,共4页Journal of Liaoning Petrochemical University

基　　金：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)

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。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.

关 键 词：微分算子 辛空间 Lagrangian子流型 奇异点 直和空间 

分 类 号：O175.3[理学—数学]