| Structure of the spectrum of infinite dimensional Hamiltonian operators |
| |
| 作者单位： | Department of |
| |
| 摘 要： | This paper deals with the structure of the spectrum of infinite dimensional Hamiltonian operators.It is shown that the spectrum,the union of the point spectrum and residual spectrum,and the continuous spectrum are all symmetric with respect to the imaginary axis of the complex plane. Moreover,it is proved that the residual spectrum does not contain any pair of points symmetric with respect to the imaginary axis;and a complete characterization of the residual spectrum in terms of the point spectrum is then given.As applications of these structure results,we obtain several necessary and sufficient conditions for the residual spectrum of a class of infinite dimensional Hamiltonian operators to be empty.
|
| 收稿时间： | 26 March 2007 |
| 修稿时间： | 29 August 2007 |
Structure of the spectrum of infinite dimensional Hamiltonian operators |
| |
| Authors: | Alatancang JunJie Huang and XiaoYing Fan |
| |
| Institution: | (1) Department of Mathematics, College of Sciences and Technology, Inner Mongolia University, Hohhot, 010021, China |
| |
| Abstract: | This paper deals with the structure of the spectrum of infinite dimensional Hamiltonian operators.It is shown that the spectrum,the union of the point spectrum and residual spectrum,and the continuous spectrum are all symmetric with respect to the imaginary axis of the complex plane. Moreover,it is proved that the residual spectrum does not contain any pair of points symmetric with respect to the imaginary axis;and a complete characterization of the residual spectrum in terms of the point spectrum is then given.As applications of these structure results,we obtain several necessary and sufficient conditions for the residual spectrum of a class of infinite dimensional Hamiltonian operators to be empty. |
| |
| Keywords: | non-self-adjoint operator infinite dimensional Hamiltonian operator structure of spectrum |
| 本文献已被 CNKI SpringerLink 等数据库收录！ |
