Generalized Lagrange Identity for Discrete Symplectic Systems and Applications in Weyl–Titchmarsh Theory

Abstract

In this paper we consider discrete symplectic systems with analytic dependence on the spectral parameter. We derive the Lagrange identity, which plays a fundamental role in the spectral theory of discrete symplectic and Hamiltonian systems. We compare it to several special cases well known in the literature. We also examine the applications of this identity in the theory of Weyl disks and square summable solutions for such systems. As an example we show that a symplectic system with the exponential coefficient matrix is in the limit point case.