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)

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.