高阶常微分算子特征值的重数关系 |
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引用本文: | 施德才,黄振友.高阶常微分算子特征值的重数关系[J].数学学报,2010,53(4):763-772. |
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作者姓名: | 施德才 黄振友 |
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作者单位: | 南京理工大学数学与应用数学系 南京 210094 |
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基金项目: | 南京理工大学发展基金资助项目(XKF09049) |
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摘 要: | 本文借助于边条件空间的几何结构,证明了自伴的高阶常微分算子特征值的解析重数等于几何重数,这是对常型Sturm-Liouville问题相关结果的一个推广.
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关 键 词: | 高阶常微分算子 自伴边条件 解析重数及几何重数 |
收稿时间: | 2009-08-21 |
修稿时间: | 2010-01-20 |
Relationships of Multiplicities of a High-Order Ordinary Differential Operator Eigenvalue |
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Institution: | Department of Mathematics and Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, P. R. |
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Abstract: | In this paper, by virtue of the geometric structure on the space of boundary conditions, we prove the equality between analytic and geometric multiplicities of a self-adjoint high-order ordinary differential operator, which is an analogue to the case of the regular Sturm--Liouville problem. |
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Keywords: | high-order eigenvalue problems self-adjoint boundary conditions equality of analytic and geometric multiplicities |
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