具有内部奇异点的微分算子自共轭域的实参数解描述

Characterization of Real-parameter Solutions of Domains of Self-adjoint Ordinary Differential Operators with Interior Singular Points

本文研究一类带有内部奇异点的微分算子的自共轭域.通过构造相应的直和空间,应用直和空间的相关理论及对相应最大算子域进行分解,在直和空间上生成的相应最小算子具有实正则型域的情形下,利用微分方程的实参数解给出此类算子的自共轭域的完全解析描述,并且确定其边界条件的矩阵仅由微分方程的解在正则点的初始值决定.

：In this paper a class of symmetric differential operators which have finite inte- rior singular points are investigated. For the purpose we constructed a direct sum space. By the theory of direct sum space and the decomposition of the corresponding maximal domain, we give the complete and analytic characterization for self-adjoint domains of symmetric dif- ferential expressions by means of the real-parametersolutions of equation τ（y） = λ0y with λ0 ∈П（To （τ）） ∩ R. T0（τ） is the corresponding minimal operator generated on the direct sum space. And the matrix defined the boundary conditions is only determined by the initial values of the regular points of the solutions.