A Theorem on C0 Semigroups Generated by Upper-triangular-type Infinite Dimensional Hamiltonian Operators
Jie Liu · Journal of Inner Mongolia University · 2009
The problem that the upper-triangular-type infinite dimensional Hamiltonian operators generate semigroups is investigated,and a sufficient condition of generating semigroups is obtained.The results are applied to the upper-triangular-type infinite dimensional Hamiltonian operators generated by a class of initial valve problem of second order constant coefficient parabolic PDEs,and it is showed that these operators generate semigroups.Furthermore,the expression of a semigroup generated by this class of Hamiltonian operators is given.So,the correctness of the results are further demonstrated.