| 具有转移条件2n阶微分算子自共轭的充要条件 |
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| 引用本文： | 张新艳,孙炯.具有转移条件2n阶微分算子自共轭的充要条件[J].数学的实践与认识,2011,41(4). |
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| 作者姓名： | 张新艳 孙炯 |
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| 作者单位： | 1. 内蒙古大学,数学科学学院,内蒙古,呼和浩特,010021;内蒙古财经学院,统计与数学学院,内蒙古,呼和浩特,010070
2. 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： | 构建了一个新的Hilbert空间,并在此空间上给出了直接由边界条件及转移条件的系数矩阵来判定2n阶微分算子自共轭的充分必要条件,即2n阶算子T是自共轭的当且仅当AJ~(-1)A~*=BJ~(-1)B~*且CJ~(-1)C~*=DJ~(-1)D~*,且C,D是2n阶复矩阵,这与二阶的情形是不同的.
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| 关 键 词： | 转移条件 自共轭性 2n阶微分算子 |
The Necessary and Sufficient Conditions of the Self-adjointness of 2n-order Differential Operators Wwith Transmission Conditions |
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| ZHANG Xin-yan,SUN Jiong.The Necessary and Sufficient Conditions of the Self-adjointness of 2n-order Differential Operators Wwith Transmission Conditions[J].Mathematics in Practice and Theory,2011,41(4). |
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| Authors: | ZHANG Xin-yan SUN Jiong |
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| Institution: | ZHANG Xin-yan~(1,2),SUN Jiong~1 (1.School of Mathematical Science,Inner Mongolia University,Hohhot 010021,China) (2.College of Statistics and Mathematics,Inner Mongolia Finance and Economics College,Hohhot 010070,China) |
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| Abstract: | We suggest a new suitable Hilbert space,and in this space we give the necessary and sufficient conditions of the self-adjointness of 2n-order differential operators by the coefficient matrix of boundary conditions and transmission conditions,i.e.2n-order differential operators is self-adjoint if and only if AJ~(-1)A~*=BJ~(-1)B~* and CJ~(-1)C~*=DJ~(-1)D~*,and C,D are 2n-order complex matrix,this is different from the case of 2-order. |
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| Keywords: | transmission conditions self-adjointness 2n-order differential operators |
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