Sturm-Liouville operators with periodically modulated parameters. Part I: Regular case
Spectral Theory
2026-04-21 v2 Mathematical Physics
Classical Analysis and ODEs
math.MP
Abstract
We introduce a new class of Sturm-Liouville operators with periodically modulated parameters. Their spectral properties depend on the monodromy matrix of the underlying periodic problem computed for the spectral parameter equal to . Under certain assumptions, by studying the asymptotic behavior of Christoffel functions and density of states, we prove that the spectral density is a continuous positive everywhere function on the real line.
Cite
@article{arxiv.2507.12300,
title = {Sturm-Liouville operators with periodically modulated parameters. Part I: Regular case},
author = {Grzegorz Świderski and Bartosz Trojan},
journal= {arXiv preprint arXiv:2507.12300},
year = {2026}
}
Comments
51 pages