辛矩阵和四阶微分算子自共轭边界条件的基本型

Symplectic Matrix and Fundamental Forms of Self-Adjoint Boundary Conditions for Differential Operators of Order Four

给出了辛矩阵的定义,讨论了它的性质,并通过使用辛矩阵的方法研究四阶自共轭的边界条件,得到了四阶自共轭边界条件的基本型,从而使得其它各种自共轭的边界条件都可以通过基本型的辛变换得到.

We give a new definition of symplectic matrix,and discuss its properties.Using methods of symplectic matrix for fourth order self-adjoint boundary conditions,we obtain the fundamental forms of self-adjoint boundary conditions,such that all other forms can be generated by the symplectic transformations of the fundamental form.