Generalized Lagrange identity for discrete symplectic systems and applications in Weyl-Titchmarsh theory
| Authors | |
|---|---|
| Year of publication | 2014 |
| Type | Article in Proceedings |
| Conference | Theory and Applications of Difference Equations and Discrete Dynamical Systems |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1007/978-3-662-44140-4_10 |
| Field | General mathematics |
| Keywords | Discrete symplectic system; Lagrange identity; L2-solution; Limit point case; Limit circle case; Weyl-Titchmarch theory |
| Attached files | |
| Description | 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. |
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