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.