## Discrete symplectic systems, boundary triplets, and self-adjoint extensions

### Volume 579 / 2022

#### Abstract

An explicit characterization of all self-adjoint extensions of the minimal linear relation associated with a discrete symplectic system is provided using the theory of boundary triplets with special attention paid to the quasiregular and limit point cases. A particular example of the system (the second order Sturm–Liouville difference equation) is also investigated thoroughly, while higher order equations or linear Hamiltonian difference systems are discussed briefly. Moreover, the corresponding gamma field and Weyl relations are established and their connection with the Weyl solution and the classical $M(\lambda)$-function is discussed. To make the paper reasonably self-contained, an extensive introduction to the theory of linear relations, self-adjoint extensions, and boundary triplets is included.