一类Hamilton 算子的重数和完备性及其应用

数学物理学报 ›› 2014, Vol. 34 ›› Issue (6): 1507-1517.

一类Hamilton 算子的重数和完备性及其应用

王华¹|阿拉坦仓^2,3|黄俊杰^2*

1.内蒙古工业大学理学院呼和浩特 010051|
2.内蒙古大学数学科学学院呼和浩特 010021;
3.呼和浩特民族学院呼和浩特 010051

收稿日期:2013-04-25 修回日期:2014-06-13 出版日期:2014-12-25 发布日期:2014-12-25
通讯作者: 黄俊杰,hjjwh@sina.com E-mail:hjjwh@sina.com
基金资助:
国家自然科学基金(11261034, 11461049, 11371185)、内蒙古自然科学基金杰出青年项目(2014MS0113, 2013JQ01, 2013ZD01)和内蒙古自治区高等学校青年科技英才支持计划(NJYT-12-B06)资助

Multiplicity and Completeness of a Class of |Hamiltonian |Operators and Its Applications

WANG Hua¹, Alatanchang^2,3, HUANG Jun-Jie^2*

1.College of Sciences, Inner Mongolia University of Technology, Hohhot 010051;
2.School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021;
3.Hohhot University for Nationalities, Hohhot 010051

Received:2013-04-25 Revised:2014-06-13 Online:2014-12-25 Published:2014-12-25
Contact: HUANG Jun-Jie,hjjwh@sina.com E-mail:hjjwh@sina.com
Supported by:
国家自然科学基金(11261034, 11461049, 11371185)、内蒙古自然科学基金杰出青年项目(2014MS0113, 2013JQ01, 2013ZD01)和内蒙古自治区高等学校青年科技英才支持计划(NJYT-12-B06)资助

摘要/Abstract

摘要：

对于一类Hamilton算子, 考虑其特征值的重数, 以及特征向量组和根向量组的完备性. 首先给出了特征值的几何重数、代数指标和代数重数, 再结合特征向量和根向量的辛正交性得到了特征向量组和根向量组完备的充分必要条件, 最后将上述结果应用于
板弯曲方程、平面弹性问题和Stokes流等问题中.

关键词: Hamilton算子, 特征值问题, 特征向量, 根向量, 重数, 完备性

Abstract:

In this paper, we consider the multiplicity of the eigenvalue and the completeness of the eigen and root vector system
of a class of Hamiltonian operators. The geometric multiplicity, algebraic index and algebraic multiplicity of each eigenvalue is completely determined. Based on the above properties and the symplectic orthogonality of the associated eigen and root vectors, the necessary and sufficient condition for the eigen or root vector system to be complete is obtained. Moreover, the obtained results are tested for several problems, for example, the plate bending, plane elasticity, Stokes flow.

Key words: Hamiltonian operator, Eigenvalue problem, Eigenvector, Root vector, Multiplicity Completeness

中图分类号:

47A70

王华, 阿拉坦仓, 黄俊杰. 一类Hamilton 算子的重数和完备性及其应用[J]. 数学物理学报, 2014, 34(6): 1507-1517.

WANG Hua, Alatanchang, HUANG Jun-Jie. Multiplicity and Completeness of a Class of |Hamiltonian |Operators and Its Applications[J]. Acta mathematica scientia,Series A, 2014, 34(6): 1507-1517.

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