English

On discrete symplectic systems: Associated maximal and minimal linear relations and nonhomogeneous problems

Spectral Theory 2016-08-30 v1

Abstract

In this paper we characterize the definiteness of the discrete symplectic system, study a nonhomogeneous discrete symplectic system, and introduce the minimal and maximal linear relations associated with these systems. Fundamental properties of the corresponding deficiency indices, including a relationship between the number of square summable solutions and the dimension of the defect subspace, are also derived. Moreover, a sufficient condition for the existence of a densely defined operator associated with the symplectic system is provided.

Keywords

Cite

@article{arxiv.1608.07787,
  title  = {On discrete symplectic systems: Associated maximal and minimal linear relations and nonhomogeneous problems},
  author = {Stephen Clark and Petr Zemánek},
  journal= {arXiv preprint arXiv:1608.07787},
  year   = {2016}
}