| 一类无穷维Hamilton算子根向量组的完备性 |
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| 引用本文： | 王华,黄俊杰,阿拉坦仓.一类无穷维Hamilton算子根向量组的完备性[J].数学学报,2011(4):541-552. |
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| 作者姓名： | 王华 黄俊杰 阿拉坦仓 |
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| 作者单位： | 内蒙古大学数学科学学院;内蒙古工业大学理学院; |
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| 基金项目： | 国家自然科学基金(10962004,11061019); 高等学校博士学科点专项科研基金(20070126002); 教育部春晖计划项目(Z2009-1-01010);教育部留学回国人员科研启动基金; 内蒙古自治区自然科学基金项目(200BS0101,2010MS0110)); 内蒙古大学211工程创新人才培养资助项目 |
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| 摘 要： | 本文研究主对角元为常数的无穷维Hamilton算子的特征值问题.基于次对角元乘积的特征值和特征向量的某些性质,刻画此类Hamilton算子特征值分布、特征值的代数指标、特征向量(或一阶根向量)的辛正交关系及特征向量组和根向量组在辛Hilbert空间中完备的充要条件.
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| 关 键 词： | 特征值问题 辛正交 完备性 |
Completeness of Root Vector Systems of a Class of Infinite-Dimensional Hamiltonian Operators |
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| Hua WANG School of Mathematical Sciences,Inner Mongolia University,Hohhot ,P.R.China College of Sciences,Inner Mongolia University of Technology,Hohhot ,P.R.China Jun Jie HUANG Alatancang School of Mathematical Sciences,P.R.China.Completeness of Root Vector Systems of a Class of Infinite-Dimensional Hamiltonian Operators[J].Acta Mathematica Sinica,2011(4):541-552. |
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| Authors: | Hua WANG School of Mathematical Sciences Inner Mongolia University Hohhot PRChina College of Sciences Inner Mongolia University of Technology Hohhot PRChina Jun Jie HUANG Alatancang School of Mathematical Sciences PRChina |
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| Institution: | Hua WANG School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,P.R.China College of Sciences,Inner Mongolia University of Technology,Hohhot 010051,P.R.China Jun Jie HUANG Alatancang School of Mathematical Sciences,P.R.China |
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| Abstract: | This paper deals with the eigenvalue problem of the Infinite-Dimensional Hamiltonian operators with the diagonal elements being constant.Based on certain properties of their eigenvalues and eigenvectors of the product of the off-diagonal elements, the location of their eigenvalues,symplectic orthogonal relationship between eigen or root vectors,and the completeness of the eigen or root vectors system are characterized. |
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| Keywords: | eigenvalue problem symplectic orthogonality completeness |
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