高阶微分算子在直和空间上的Friedrichs扩张的辛几何刻画

Complex Symplectic Geometry Characterization for the Friedrichs Extension of the High Order Differential Operators in Direct Sum Spaces

通过最大与最小算子域构造了一个辛空间,用辛空间中的完全Lagrangian子流形与对称微分算子自共轭扩张的一一对等关系,研究对称微分算子自共轭域的辛结构,从辛几何的角度给出直和空间上正则型高阶微分算子的Friedrichs扩张域的代数结构.

In this paper,we define symplectic spaces and their Lagrangian submanifold by the domains of the maximal and the minimal operator.Applying basic algebraic properties of Lagrangian submanifold of symplectic spaces and self-adjoint extensions of symmetric differential operators,the symplectic structure of ordinary differential operators are studied and the symplectic geometry characterization for the Friedrichs extensions domains of the minimal operators of regular high order differential operators are given in direct sum spaces.