Characterization of self-adjoint extensions for discrete symplectic systems

摘要

All self-adjoint extensions of minimal linear relation associated with thediscrete symplectic system are characterized. Especially, for the scalar caseon a finite discrete interval some equivalent forms and the uniqueness of thegiven expression are discussed and the Krein--von Neumann extension isdescribed explicitly. In addition, a limit point criterion for symplecticsystems is established. The result partially generalizes even a classical limitpoint criterion for the second order Sturm--Liouville difference equations.