无穷区间上的高阶奇型微分算子的自共轭域的辛几何刻画

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

从辛几何的角度研究定义在无穷区间上高阶奇型对称微分算子的辛结构,利用最大与最小算子域构造了一个辛空间,用辛空间中的线性流形来刻画定义在无穷区间上高阶奇型对称微分算子的自共轭扩张问题.给出了与微分算子自共轭域相联系的相应的Lagrangian子流形的描述和分类情况,等价于对微分算子l(y)的自共轭域进行描述.

The symplectic geometry description of the self-adjoint domains of higher order differential operators defined in an infinite interval is studied in terms of the symplectic geometry. A symplectie space is constructed by the domain of maximal operator and the domain of minimal operator. By using linear submanifold, the self-adjoint domains of higher order differential operators defined in an infinite interval are described. The description of Lagrangian submanifold and the classification related to the self-adjoint domains are presented and this description is equal to that of the self-adjoint domains of l（y）.