四阶常微分算子特征值的重数相等

Equality of Multiplicities of a 4-Order Ordinary Differential Operator Eigenvalue

借助解析重数和几何重数的基本定义及边界条件的几何结构,证明了自伴的四阶常微分算子特征值的解析重数与几何重数是相等的,该结论是对常型Sturm-Liouville问题相关结果的推广.

By virtue of analytic and geometric multiplicities＇ basic definition and the geometric structure on the space of boundary conditions,the equality between analytic and geometric multiplicities of an adjoint forth-order ordinary differential operator are proved,which is an analogue to the case of the regular Sturm-Liouville problem.