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 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.
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}
}