English

The Friedrichs extension of a class of discrete symplectic systems

Spectral Theory 2024-12-23 v1

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.

Keywords

Cite

@article{arxiv.2412.16096,
  title  = {The Friedrichs extension of a class of discrete symplectic systems},
  author = {Petr Zemánek},
  journal= {arXiv preprint arXiv:2412.16096},
  year   = {2024}
}