| 微分方程解刻画的实系数对称微分算子的自共轭域 |
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| 引用本文： | 郝晓玲,孙炯.微分方程解刻画的实系数对称微分算子的自共轭域[J].数学的实践与认识,2010,40(6). |
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| 作者姓名： | 郝晓玲 孙炯 |
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| 作者单位： | 内蒙古大学,数学科学学院,内蒙古,呼和浩特,010021 |
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| 基金项目： | 国家自然科学基金(10861008) |
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| 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.
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| 关 键 词： | 微分算子 亏指数 自共轭域 实参数解 |
The Self-Adjoint Domains of Symmetric Differential Expressions with Real-valued Coefficients Described by Solutions of Ordinary Differential Equations |
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| HAO Xiao-ling,SUN Jiong.The Self-Adjoint Domains of Symmetric Differential Expressions with Real-valued Coefficients Described by Solutions of Ordinary Differential Equations[J].Mathematics in Practice and Theory,2010,40(6). |
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| Authors: | HAO Xiao-ling SUN Jiong |
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| Institution: | HAO Xiao-ling,SUN Jiong (School of Mathematical Science,Inner Mongolia University,Hohhot 010021,China) |
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| Abstract: | 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. |
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| Keywords: | differential operator deficiency index self-adjoint domain real-parameter solution |
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