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What is the most general form of the Sturm oscillation theorem?

So far I have only seen cases that treat either unbounded intervals or weighted $L^2$ spaces. I would be especially interested in something that works for semi-bounded self-adjoint (Sturm-Liouville) operators $A:D(A)\to L^2_\rho([0,\infty))$ with some arbitrary weight $\rho$.

I am aware of the very approachable paper by Simon, I guess I could redo the same proof with weights but there are some parts in his proof that are still not entirely clear to me.

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  • $\begingroup$ I don't know the most general form of Sturm Oscillation Theorem, but it may be worth looking at "Oscillation Theory" by Kreith which contains results of this nature. Additionally, oscillation theorems are proved in "Maximum Principles in Differential Equations" by Protter and Weinberger. Both of these books should contain further references which can also be investigated. $\endgroup$
    – JCM
    Commented Jul 8, 2016 at 13:36

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