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

Grzegorz Świderski; Bartosz Trojan

doi:10.1016/j.jde.2026.114188

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arXiv · 2507.12300

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

Grzegorz Świderski·Bartosz Trojan

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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.

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BibTeX RIS

Grzegorz Świderski, Bartosz Trojan. 2025-07-16. Sturm-Liouville operators with periodically modulated parameters. Part I: Regular case. https://doi.org/10.1016/j.jde.2026.114188

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