Sturm-Liouville operators with periodically modulated parameters. Part I: Regular case

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 $0$. 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.