直和空间上对称微分算子自共轭域的辛几何刻画(Ⅳ)

Symplectic Geometry Characterization of Self-Adjoint Domainsfor Symmetric Differential Operators in Direct Sum Spaces(Ⅳ)

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取中间亏指数时,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。给出了与高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。

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 middle deficiency indices singular points were studied.The classification and description of complete Lagrangian subman-ifold that correspond with self-adjoint domains of second order differential operators were given.