Characterization of self-adjoint extensions for discrete symplectic systems

Abstract

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

References in corpus (1)

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

Cited by in corpus (4)

• Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter
• Discrete Dirac systems on the semiaxis: rational reflection coefficients and Weyl functions
• Resolvent and spectrum for discrete symplectic systems in the limit point case
• Canonical forms for boundary conditions of self-adjoint differential operators