Block basis property of a class of 2×2 operator matrices and its application to elasticity

doi:10.1088/1674-1056/22/9/094601

中国物理B ›› 2013, Vol. 22 ›› Issue (9): 94601-094601.doi: 10.1088/1674-1056/22/9/094601

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Block basis property of a class of 2×2 operator matrices and its application to elasticity

宋宽, 侯国林, 阿拉坦仓

School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China

收稿日期:2013-03-12 修回日期:2013-04-02 出版日期:2013-07-26 发布日期:2013-07-26
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11361034 and 11371185), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20111501110001), and the Natural Science Foundation of Inner Mongolia, China (Grant Nos. 2012MS0105 and 2013ZD01 ).

Block basis property of a class of 2×2 operator matrices and its application to elasticity

Song Kuan (宋宽), Hou Guo-Lin (侯国林), Alatancang (阿拉坦仓)

School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China

Received:2013-03-12 Revised:2013-04-02 Online:2013-07-26 Published:2013-07-26
Contact: Hou Guo-Lin E-mail:smshgl@imu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11361034 and 11371185), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20111501110001), and the Natural Science Foundation of Inner Mongolia, China (Grant Nos. 2012MS0105 and 2013ZD01 ).

摘要/Abstract

摘要： A necessary and sufficient condition is obtained for the generalized eigenfunction systems of 2×2 operator matrices to be a block Schauder basis of some Hilbert space, which offers a mathematical foundation of solving symplectic elasticity problems by using the method of separation of variables. Moreover, the theoretical result is applied to two plane elasticity problems via the separable Hamiltonian systems.

关键词: symplectic elasticity, block Schauder basis, separable Hamiltonian system, operator matrices

Abstract: A necessary and sufficient condition is obtained for the generalized eigenfunction systems of 2×2 operator matrices to be a block Schauder basis of some Hilbert space, which offers a mathematical foundation of solving symplectic elasticity problems by using the method of separation of variables. Moreover, the theoretical result is applied to two plane elasticity problems via the separable Hamiltonian systems.

Key words: symplectic elasticity, block Schauder basis, separable Hamiltonian system, operator matrices

中图分类号: (Static elasticity)

46.25.-y

02.30.Jr (Partial differential equations) 02.30.Tb (Operator theory)

宋宽, 侯国林, 阿拉坦仓. Block basis property of a class of 2×2 operator matrices and its application to elasticity[J]. 中国物理B, 2013, 22(9): 94601-094601.

Song Kuan (宋宽), Hou Guo-Lin (侯国林), Alatancang (阿拉坦仓). Block basis property of a class of 2×2 operator matrices and its application to elasticity[J]. Chin. Phys. B, 2013, 22(9): 94601-094601.

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Block basis property of a class of 2×2 operator matrices and its application to elasticity

Block basis property of a class of 2×2 operator matrices and its application to elasticity

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