English

Oscillation theory and semibounded canonical systems

Spectral Theory 2018-11-20 v1

Abstract

Oscillation theory locates the spectrum of a differential equation by counting the zeros of its solutions. We present a version of this theory for canonical systems Ju=zHuJu'=-zHu and then use it to discuss semibounded operators from this point of view. Our main new result is a characterization of systems with purely discrete spectrum in terms of the asymptotics of their coefficient functions; we also discuss the exponential types of the transfer matrices.

Keywords

Cite

@article{arxiv.1811.07067,
  title  = {Oscillation theory and semibounded canonical systems},
  author = {Christian Remling and Kyle Scarbrough},
  journal= {arXiv preprint arXiv:1811.07067},
  year   = {2018}
}
R2 v1 2026-06-23T05:18:49.699Z