无穷区间上的二阶奇型对称微分算子自共轭域的辛几何刻画

The Symplectic Geometry Description of the Self-adjoint Domains of 2-nd Order Symmetric Differential Operators on Infinite Interval

从辛几何的角度研究了定义在无穷区间上二阶奇型对称微分算子的代数结构.首先,构造了与二阶微分算子相关联的辛空间.然后给出了与微分算子自共轭域相联系的相应的La-grangian子流形的描述和分类情况,这就等价于对l(y)的自共轭域进行描述.

The basic algebraic properties of the self-adjoint domains of 2-nd order differential operators defined in an infinite interval is investigated by symplectic geometry.Frist,a symplectic space about the 2-nd order differential operator is constructed.Then using Lagrangian submanifold of the symplectic space,a complete discription of the self-adjoint domains and their classification s obtained.