On the completeness of eigen and root vector systems for fourth-order operator matrices and their applications

doi:10.1088/1674-1056/20/10/100202

中国物理B ›› 2011, Vol. 20 ›› Issue (10): 100202-100202.doi: 10.1088/1674-1056/20/10/100202

On the completeness of eigen and root vector systems for fourth-order operator matrices and their applications

阿拉坦仓¹, 黄俊杰¹, 王华²

(1)School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China; (2)School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China; College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China

收稿日期:2011-01-27 修回日期:2011-06-05 出版日期:2011-10-15 发布日期:2011-10-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11061019 and 10962004), the Chunhui Program of Ministry of Education of China (Grant No. Z2009-1-01010), the Natural Science Foundation of Inner Mongolia, China (Grant Nos. 2010MS0110 and 2009BS0101), and the Cultivation of Innovative Talent of ‘211 Project’ of Inner Mongolia University.

On the completeness of eigen and root vector systems for fourth-order operator matrices and their applications

Wang Hua(王华)^a)b), Alatancang (阿拉坦仓)^a), and Huang Jun-Jie(黄俊杰)^a)†

^a School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China; ^b College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China

Received:2011-01-27 Revised:2011-06-05 Online:2011-10-15 Published:2011-10-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11061019 and 10962004), the Chunhui Program of Ministry of Education of China (Grant No. Z2009-1-01010), the Natural Science Foundation of Inner Mongolia, China (Grant Nos. 2010MS0110 and 2009BS0101), and the Cultivation of Innovative Talent of ‘211 Project’ of Inner Mongolia University.

摘要/Abstract

摘要： In this paper, we consider the eigenvalue problem of a class of fourth-order operator matrices appearing in mechanics, including the geometric multiplicity, algebraic index, and algebraic multiplicity of the eigenvalue, the symplectic orthogonality, and completeness of eigen and root vector systems. The obtained results are applied to the plate bending problem.

关键词: operator matrix, eigenvalue problem, eigenvector, root vector, completeness

Abstract: In this paper, we consider the eigenvalue problem of a class of fourth-order operator matrices appearing in mechanics, including the geometric multiplicity, algebraic index, and algebraic multiplicity of the eigenvalue, the symplectic orthogonality, and completeness of eigen and root vector systems. The obtained results are applied to the plate bending problem.

Key words: operator matrix, eigenvalue problem, eigenvector, root vector, completeness

中图分类号: (Operator theory)

02.30.Tb

02.30.Jr (Partial differential equations) 46.25.-y (Static elasticity)

王华, 阿拉坦仓, 黄俊杰. On the completeness of eigen and root vector systems for fourth-order operator matrices and their applications[J]. 中国物理B, 2011, 20(10): 100202-100202.

Wang Hua(王华), Alatancang (阿拉坦仓), and Huang Jun-Jie(黄俊杰) . On the completeness of eigen and root vector systems for fourth-order operator matrices and their applications[J]. Chin. Phys. B, 2011, 20(10): 100202-100202.

参考文献 12

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[12]	Wang H, Alatancang and Huang J J 2011 Acta Math. Sin. 54 541 (in Chinese)

On the completeness of eigen and root vector systems for fourth-order operator matrices and their applications

On the completeness of eigen and root vector systems for fourth-order operator matrices and their applications

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