Generalized Lagrange Identity for Discrete Symplectic Systems and Applications in Weyl–Titchmarsh Theory
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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.
KeywordsLagrange Identity Symplectic System Discrete Symplectic Weyl Titchmarsh Theory Weyl Discs
The first author was supported by the Czech Science Foundation under grant P201/10/1032. The second author was supported by the Program of “Employment of Newly Graduated Doctors of Science for Scientific Excellence” (grant number CZ.1.07/2.3.00/30.0009) co-financed from European Social Fund and the state budget of the Czech Republic.
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