| 微分算子的对称扩张及Friedrichs扩张的辛几何刻画 |
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| 引用本文： | 杨传富,黄振友,杨孝平. 微分算子的对称扩张及Friedrichs扩张的辛几何刻画[J]. 数学学报, 2006, 49(2): 421-430. DOI: cnki:ISSN:0583-1431.0.2006-02-022 |
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| 作者姓名： | 杨传富 黄振友 杨孝平 |
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| 作者单位： | 南京理工大学应用数学系,南京210094 |
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| 摘 要： | 本文在加权Hilbert空间L2(I,r(x))(I=(a,6),-∞≤a 0)中,利用辛几何,刻画了n阶对称微分算式的最小算子的对称扩张(含自伴扩张)及 Friedrichs扩张,分别获得了其扩张为对称扩张、Friedrichs扩张的充分必要条件．
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| 关 键 词： | 辛几何 Lagrange子流形 微分算子 |
| 文章编号： | 0583-1431（2006）02-0421-10 |
| 收稿时间： | 2003-11-11 |
| 修稿时间： | 2003-11-112005-03-08 |
Complex Symplectic Geometry Characterizations for Symmetric Extensions and Priedrichs Extensions of Differential Operators |
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| Chuan Fu YANG ,Zhen You HUANG ,Xiao Ping YANG. Complex Symplectic Geometry Characterizations for Symmetric Extensions and Priedrichs Extensions of Differential Operators[J]. Acta Mathematica Sinica, 2006, 49(2): 421-430. DOI: cnki:ISSN:0583-1431.0.2006-02-022 |
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| Authors: | Chuan Fu YANG Zhen You HUANG Xiao Ping YANG |
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| Affiliation: | Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, P. R. China |
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| Abstract: | In this paper, we give complex symplectic geometry characterizations for symmetric extensions (including self-adjoint extensions) and Priedrichs extension of the minimal operator generated by nth-order symmetric differential expression, defined in the weighted Hilbert space L2(I,r(x)) (the non-degenerate interval I, with endpoints -∞≤a,b≤∞). The necessary and sufficient conditions which ensure that its extensions are symmetric extensions, Priedrichs extension are obtained respectively. |
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| Keywords: | symplectic geometry Lagrangian submanifold differential operator |
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