Resolvent and spectrum for discrete symplectic systems in the limit point case

Abstract

The spectrum of an arbitrary self-adjoint extension of the minimal linear relation associated with the discrete symplectic system in the limit point case is completely characterized by using the limiting Weyl--Titchmarsh $M_{+}(\lambda )$-function. Furthermore, a dependence of the spectrum on a boundary condition is investigated and, consequently, several results of the singular Sturmian theory are derived.

References in corpus (3)

• On discrete symplectic systems: Associated maximal and minimal linear relations and nonhomogeneous problems
• Characterization of self-adjoint extensions for discrete symplectic systems
• Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter

Cited by in corpus (1)

• On classification of singular matrix difference equations of mixed order