Invariance of deficiency indices under perturbation for discrete Hamiltonian systems

Abstract

This paper deals with discrete Hamiltonian systems with one singular endpoint. Using Hermitian linear relation generalized by linear Hamiltonian system, the invariance of the minimal and maximal deficiency indices under bounded perturbation for discrete Hamiltonian systems is built. This parallels the well-known results for linear Hamiltonian differential systems obtained by F.V. Atkinson.

Keywords:

• discrete Hamiltonian system
• deficiency index
• linear relation
• invariance
• perturbation

2000 Mathematics Subject Classification::

• 34L05
• 39A70
• 47E05

Acknowledgements

The author sincerely thanks the referee for the constructive suggestions and corrections. This research was partially supported by the NNSF of China (Grants 11271225, 11171178) and NSF of Shandong (Grant ZR2009AQ010).