两个高阶正则拟微分算子积的对称性  

On Symmetry of the Product of Two Higher-Order Regular Quasi-Differential Operators

作　　者：向延誉 王爱平 Xiang Yanyu;Wang Aiping(North China Electric Power University,School of Mathematics and Physics,Beijing 102206)

机构地区：[1]华北电力大学数理学院,北京102206

出　　处：《数学物理学报（A辑）》2024年第2期265-275,共11页Acta Mathematica Scientia

摘　　要：研究了在Hilbert空间中两个一般的正则拟微分算式乘积的对称实现问题,刻画了由其确定对称算子的两点边界条件,得到两个高阶正则微分算子的乘积算子是对称算子的充分必要条件,所得结论包括了乘积算子的自共轭域的刻画这一结果作为其特殊情形.给出了乘积算子为对称算子的几个例子.The symmetric realizations of the product of two general regular quasi-differential expressions in Hilbert space are investigated.The two-point boundary conditions which determine symmetric operators are characterized and a suficient and necessary condition for the product of two higher-order regular differential operators to be symmetric is obtained.The presented result contains the self-adjoint do-main characterization as a special case.Several examples of regular symmetric product operators aregiven.

关 键 词：拟微分算式 对称算子的积 边界条件 对称算子 

分 类 号：O175.3[理学—数学]