Essential spectrum of singular discrete linear Hamiltonian systems.
- Resource Type
- Article
- Authors
- Sun, Huaqing; Kong, Qingkai; Shi, Yuming
- Source
- Mathematische Nachrichten. Feb2016, Vol. 289 Issue 2-3, p343-359. 17p.
- Subject
- *HAMILTONIAN systems
*HERMITIAN operators
*WEYL space
*JACOBI operators
*LINEAR operators
*SUBSPACES (Mathematics)
- Language
- ISSN
- 0025-584X
The paper is concerned with the essential spectral points of singular discrete linear Hamiltonian systems. Several sufficient conditions for a real point to be in the essential spectrum are obtained in terms of the number of linearly independent square-summable solutions of the corresponding homogeneous linear system, and a sufficient and necessary condition for a real point to be in the essential spectrum is given in terms of the number of linearly independent square-summable solutions of the corresponding nonhomogeneous linear system. As a direct consequence, the corresponding results for singular higher-order symmetric vector difference expressions are given. [ABSTRACT FROM AUTHOR]