On symplectic self-adjointness of Hamiltonian operator matrices  

作　　者：CHEN Alatancang JIN GuoHai WU DeYu 

机构地区：[1]School of Mathematical Sciences, Inner Mongolia University [2]Department of Mathematics, Hohhot University for Nationalities

出　　处：《Science China Mathematics》2015年第4期821-828,共8页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11371185,11101200 and 11361034);Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20111501110001);Major Subject of Natural Science Foundation of Inner Mongolia of China(Grant No.2013ZD01);Natural Science Foundation of Inner Mongolia of China(Grant No.2012MS0105)

摘　　要：Symplectic self-adjointness of Hamiltonian operator matrices is studied, which is important to symplectic elasticity and optimal control. For the cases of diagonal domain and off-diagonal domain, necessary and sufficient conditions are shown. The proofs use Frobenius-Schur factorizations of unbounded operator matrices.Under additional assumptions, sufficient conditions based on perturbation method are obtained. The theory is applied to a problem in symplectic elasticity.Symplectic self-adjointness of Hamiltonian operator matrices is studied, which is important to symplectic elasticity and optimal control. For the cases of diagonal domain and off-diagonal domain, necessary and sufficient conditions are shown. The proofs use Frobenius-Schur factorizations of unbounded operator matrices.Under additional assumptions, sufficient conditions based on perturbation method are obtained. The theory is applied to a problem in symplectic elasticity.

关 键 词：symplectic elasticity symplectic self-adjoint Hamiltonian operator matrix 

分 类 号：O151.21[理学—数学]