两个高阶正则拟微分算子积的对称性

摘要/Abstract

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.

关键词: 拟微分算式, 对称算子的积, 边界条件, 对称算子

Abstract:

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 sufficient 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 are given.

Key words: Quasi-Differential expressions, Product of differential operators, Boundary conditions, Symmetric operators

中图分类号:

O175.3

向延誉, 王爱平. 两个高阶正则拟微分算子积的对称性[J]. 数学物理学报, 2024, 44(2): 265-275.

Xiang Yanyu, Wang Aiping. On Symmetry of the Product of Two Higher-Order Regular Quasi-Differential Operators[J]. Acta mathematica scientia,Series A, 2024, 44(2): 265-275.

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