Eigenvalue problem of Hamiltonian operator matrices

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• 作者：Hua Wang (1)
  Junjie Huang (2)
  Alatancang Chen (2)
  
  1. College of Sciences ; Inner Mongolia University of Technology ; Hohhot ; 010051 ; P.R. China
  2. School of Mathematical Sciences ; Inner Mongolia University ; Hohhot ; 010021 ; P.R. China
  
• 关键词：47A70 ; 47A75 ; Hamiltonian operator matrix ; algebraic multiplicity ; eigenvector ; root vector ; completeness
• 刊名：Journal of Inequalities and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,135 KB
• 参考文献：1. Zhong, W (1991) Method of separation of variables and Hamiltonian system. Comput. Struct. Mech. Appl. 8: pp. 229-239
  2. Zhong, W (2004) Duality System in Applied Mechanics and Optimal Control. Kluwer Academic, Dordrecht
  3. Stephen, NG, Ghosh, S (2005) Eigenanalysis and continuum modelling of a curved repetitive beam-like structure. Int. J.聽Mech. Sci. 47: pp. 1854-1873 CrossRef
  4. Chen, JT, Lee, YT, Lee, JW (2010) Torsional rigidity of an elliptic bar with multiple elliptic inclusions using a null-field integral approach. Comput. Mech. 46: pp. 511-519 CrossRef
  5. Yao, W, Zhong, W, Lim, CW (2009) Symplectic Elasticity. World Scientific, Singapore CrossRef
  6. Leung, AYT, Xu, X, Gu, Q (2007) The boundary layer phenomena in two-dimensional transversely isotropic piezoelectric media by exact symplectic expansion. Int. J. Numer. Methods Eng. 69: pp. 2381-2408 CrossRef
  7. Kurina, GA (2001) Invertibility of nonnegatively Hamiltonian operators in a Hilbert space. Differ. Equ. 37: pp. 880-882 CrossRef
  8. Kurina, GA, Roswitha, M (2004) On linear-quadratic optimal control problems for time-varying descriptor systems. SIAM J.聽Control Optim. 42: pp. 2062-2077 CrossRef
  9. Huang, J, Alatancang, , Chen, A (2008) Completeness for the eigenfunction system of a class of infinite dimensional Hamiltonian operators. Acta Math. Appl. Sin. 31: pp. 457-466
  10. Alatancang, , Wu, D (2009) Completeness in the sense of Cauchy principal value of the eigenfunction systems of infinite dimensional Hamiltonian operator. Sci. China Ser. A 52: pp. 173-180 CrossRef
  11. Langer, H, Ran, ACM, Rotten, BA (2001) Invariant subspaces of infinite dimensional Hamiltonians and solutions of the corresponding Riccati equations. Linear Operators and Matrices. Birkh盲user, Basel
  12. Huang, J, Alatancang, , Wu, H (2010) Descriptions of spectra of infinite dimensional Hamiltonian operators and their applications. Math. Nachr. 283: pp. 541-552
  13. Alatancang, , Huang, J, Fan, X (2008) Structure of the spectrum for infinite dimensional Hamiltonian operators. Sci. China Ser.聽A 51: pp. 915-924 CrossRef
  14. Azizov, TY, Dijksma, A, Gridneva, IV (2002) On the boundedness of Hamiltonian operators. Proc. Am. Math. Soc. 131: pp. 563-576 CrossRef
  15. Wang, H, Huang, J, Alatancang, (2011) Completeness of root vector systems of a class of infinite-dimensional Hamiltonian operators. Acta Math. Sin. 54: pp. 541-552
  16. Gohberg, IC, Kre谋虒n, MG (1969) Introduction to the Theory of Linear Nonselfadjoint Operators. Am. Math. Soc., Providence
  17. Taylor, AE (1966) Theorems on ascent, descent, nullity and defect of linear operators. Math. Ann. 163: pp. 18-49 CrossRef
  
• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

This paper deals with the eigenvalue problem of Hamiltonian operator matrices with at least one invertible off-diagonal entry. The ascent and the algebraic multiplicity of their eigenvalues are determined by using the properties of the eigenvalues and associated eigenvectors. The necessary and sufficient condition is further given for the eigenvector (root vector) system to be complete in the Cauchy principal value sense.