Spectral theory of discrete linear Hamiltonian systems |
| |
Authors: | Yuming Shi |
| |
Affiliation: | Department of Mathematics, Shandong University, Jinan, Shandong 250100, People's Republic of China |
| |
Abstract: | This paper is concerned with spectral problems for a class of discrete linear Hamiltonian systems with self-adjoint boundary conditions, where the existence and uniqueness of solutions of initial value problems may not hold. A suitable admissible function space and a difference operator are constructed so that the operator is self-adjoint in the space. Then a series of spectral results are obtained: the reality of eigenvalues, the completeness of the orthogonal normalized eigenfunction system, Rayleigh's principle, the minimax theorem and the dual orthogonality. Especially, the number of eigenvalues including multiplicities and the number of linearly independent eigenfunctions are calculated. |
| |
Keywords: | Discrete linear Hamiltonian system Spectral theory Boundary value problem Self-adjoint operator |
本文献已被 ScienceDirect 等数据库收录! |
|