向量微分算子对称扩张的完全描述

Complete Description of Symmetric Extensions of Symmetric Vector-valued Differential Operators

本文根据Hilbert空间中对称算子的扩张理论,首先以抽象边条件的形式给出了向量微分算子的对称扩张特征,然后推广应用文[4,5,6]的方法,给出向量微分算子对称扩张的完全描述,概括了以前在这方面的所有结果。

In this paper,applying the extension theory of symmetric operators in Hilbert apace and using the methods of [4,5,6],we give the complete description of symmetric extensions of the minimal operator T_0 generated by the vector-valued differential expression τ introduced in [2].The domain of any seffadjoint extension of T_0 with equal finite defecciency indices and many results in [2,3,4,5,6] can be deduced from the conclusions of this paper.