Generalized Lagrange identity for discrete symplectic systems and applications in Weyl-Titchmarsh theory. (English) Zbl 1318.39008

Šimon Hilscher, Roman; Zemánek, Petr

AlSharawi, Ziyad (ed.) et al., Theory and applications of difference equations and discrete dynamical systems. ICDEA, Muscat, Oman, May 26–30, 2013. Berlin: Springer (ISBN 978-3-662-44139-8/hbk; 978-3-662-44140-4/ebook). Springer Proceedings in Mathematics & Statistics 102, 187-202 (2014).

Summary: 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.
For the entire collection see [Zbl 1297.39001].

MSC:

39A12	Discrete version of topics in analysis
37J05	Relations of dynamical systems with symplectic geometry and topology (MSC2010)

Keywords:

Weyl-Titchmarsh theory; discrete symplectic systems; Lagrange identity; Hamiltonian systems