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

作　　者：郭芳[1] 

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2008年第6期714-721,共8页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10561005);高等学校博士学科点专项科研基金资助项目(20040126008);内蒙古师范大学青年科研基金资助项目(QN06043)

摘　　要：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）.

关 键 词：高阶奇型微分算子 辛几何 lagrangian子流形 自共轭域 

分 类 号：O175.3[理学—数学]