Sturm-Liouville operators with periodically modulated parameters have spectral density that is continuous and positive everywhere on the real line under assumptions on the monodromy matrix at spectral parameter zero.
Everitt, A catalogue of Sturm-Liouville differential equations , Sturm-Liouville theory, Birkhäuser, Basel, 2005, pp
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Sturm-Liouville operators with periodically modulated parameters. Part I: Regular case
Sturm-Liouville operators with periodically modulated parameters have spectral density that is continuous and positive everywhere on the real line under assumptions on the monodromy matrix at spectral parameter zero.