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.
Clark, A spectral analysis for self-adjoint operators generated b y a class of second order difference equations , J
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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.