Generalized Inverse of Upper Triangular Infinite Dimensional Hamiltonian Operators

2013 ◽  
Vol 20 (03) ◽  
pp. 395-402
Author(s):  
Junjie Huang ◽  
Xiang Guo ◽  
Yonggang Huang ◽  
Alatancang
Keyword(s):  
Explicit Expression ◽  
Generalized Inverse ◽  
Hamiltonian Operator ◽  
Operator Matrix ◽  
Infinite Dimensional ◽  
Symplectic Spaces ◽  
Hamiltonian Operators

In this paper, we deal with the generalized inverse of upper triangular infinite dimensional Hamiltonian operators. Based on the structure operator matrix J in infinite dimensional symplectic spaces, it is shown that the generalized inverse of an infinite dimensional Hamiltonian operator is also Hamiltonian. Further, using the decomposition of spaces, an upper triangular Hamiltonian operator can be written as a new operator matrix of order 3, and then an explicit expression of the generalized inverse is given.

scholarly journals Right and Left Weyl Operator Matrices in a Banach Space Setting

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Aichun Liu ◽  
Junjie Huang ◽  
Alatancang Chen
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Sufficient Conditions ◽  
Operator Matrix ◽  
Weyl Operator ◽  
Operator Matrices ◽  
Space Setting ◽  
Hamiltonian Operators ◽  
Equivalent Conditions

Let X i , Y i i = 1,2 be Banach spaces. The operator matrix of the form M C = A C 0 B acting between X 1 ⊕ X 2 and Y 1 ⊕ Y 2 is investigated. By using row and column operators, equivalent conditions are obtained for M C to be left Weyl, right Weyl, and Weyl for some C ∈ ℬ X 2 , Y 1 , respectively. Based on these results, some sufficient conditions are also presented. As applications, some discussions on Hamiltonian operators are given in the context of Hilbert spaces.

Analytical Solutions for Laminated Transversely Isotropic Magnetoelectroelastic Plates

2013 ◽  
Vol 634-638 ◽  
pp. 2425-2431
Author(s):  
Xiao Chuan Li ◽  
Qing Li
Keyword(s):  
Symplectic Geometry ◽  
Separation Of Variables ◽  
Electric Displacement ◽  
Transversely Isotropic ◽  
Hamiltonian Operator ◽  
Hamiltonian Matrix ◽  
Operator Matrix ◽  
Zero Eigenvalue ◽  
Dual Variables ◽  
Eigen Solutions

The theory of Hamiltonian system is introduced for the problems of laminated transversely isotropic magnetoelectroelastic plates. The partial differential equations of the magnetoelectroelastic solids are derived corresponding to the Lagrange density function and Legendre’s transformation. These equations are a set of the first-order Hamiltonian equations and expressed with displacements, electric potential and magnetic potential, as well as their dual variables--lengthways stress, electric displacement and magnetic induction in the symplectic geometry space. To obtain the solutions of the equations, the schemes of separation of variables and expansion of eigenvector of Hamiltonian operator matrix in the polar direction are implemented. The homogenous solutions of the equations consist of zero eigen-solutions and nonzero eigen-solutions. All the eigen-solutions of zero eigenvalue are obtained in the symmetric deformation. These solutions give the classical Saint-Venant’s solutions because the Hamiltonian matrix is symplectic. The method is rational, analytical method and does not require any trial functions.

Symplectic Self-adjointness of Infinite Dimensional Hamiltonian Operators

2018 ◽  
Vol 34 (9) ◽  
pp. 1473-1484
Author(s):  
Lin Li ◽  
Alatancang Chen ◽  
De Yu Wu
Keyword(s):  
Infinite Dimensional ◽  
Hamiltonian Operators
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