一类无穷维Hamilton算子根向量组的完备性

王华, 黄俊杰, 阿拉坦仓

数学学报 ›› 2011, Vol. 54 ›› Issue (4) : 541-552.

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数学学报 ›› 2011, Vol. 54 ›› Issue (4) : 541-552. DOI: 10.12386/A2011sxxb0055
论文

一类无穷维Hamilton算子根向量组的完备性

    王华1,2, 黄俊杰1, 阿拉坦仓1
作者信息 +

Completeness of Root Vector Systems of a Class of Infinite-Dimensional Hamiltonian Operators

    Hua WANG1,2, Jun Jie HUANG1, Alatancang1
Author information +
文章历史 +

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.  

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.  

关键词

特征值问题 / 辛正交 / 完备性

Key words

eigenvalue problem / symplectic orthogonality / completeness

引用本文

导出引用
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. 数学学报, 2011, 54(4): 541-552 https://doi.org/10.12386/A2011sxxb0055
Hua WANG, Jun Jie HUANG, Alatancang. Completeness of Root Vector Systems of a Class of Infinite-Dimensional Hamiltonian Operators. Acta Mathematica Sinica, Chinese Series, 2011, 54(4): 541-552 https://doi.org/10.12386/A2011sxxb0055

参考文献

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基金

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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