The Friedrichs extension of a class of discrete symplectic systems

Abstract

The Friedrichs extension of minimal linear relation being bounded below and associated with the discrete symplectic system with a special linear dependence on the spectral parameter is characterized by using recessive solutions. This generalizes a similar result obtained by Do\v{s}l\'y and Hasil for linear operators defined by infinite banded matrices corresponding to even-order Sturm--Liouville difference equations and, in a certain sense, also results of Marletta and Zettl or \v{S}imon Hilscher and Zem\'anek for singular differential operators.