微分方程解刻画的实系数对称微分算子的自共轭域  

The Self-Adjoint Domains of Symmetric Differential Expressions with Real-valued Coefficients Described by Solutions of Ordinary Differential Equations

作　　者：郝晓玲[1] 孙炯[1] 

机构地区：[1]内蒙古大学数学科学学院,内蒙古呼和浩特010021

出　　处：《数学的实践与认识》2010年第6期214-222,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10861008)

摘　　要：通过把两个奇异端点的边界条件加以分离,利用微分方程的解(实参数解或复参数解)给出了实系数对称微分算子最大算子域的一种新的分解.进而应用这些解统一对其自共轭域进行描述,给出了自共轭域的完全刻画.By separating the boundary conditions of the two singular endpoints,we establish a new decomposition of the maximal domain of the symmetric differential operator with real coefficients in term of solutions of the differential equation（the real-parameter solutions or the complex-parameter solutions）.Moreover,we give the complete characterization of self-adjoint domain by these solutions.

关 键 词：微分算子 亏指数 自共轭域 实参数解 

分 类 号：O175.3[理学—数学]