The Friedrichs extension of a class of discrete symplectic systems

2024/12/20 by Zemánek, Petr
#39A06 #39A12 #47A06 #47A20 #47B39 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2412.16096

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 Došlý 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 Šimon Hilscher and Zemánek for singular differential operators.

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