【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。更多还原

【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.更多还原