Reflectionless Sturm-Liouville Equations

Details Reflectionless Sturm-Liouville Equations Reflectionless Sturm-Liouville Equations

2006-05-03

arxiv.org/abs/math-ph/0605007v1

Physics

Mathematical Physics

Scientific paper

We consider compactly supported perturbations of periodic Sturm-Liouville equations. In this context, one can use the Floquet solutions of the periodic background to define scattering coefficients. We prove that if the reflection coefficient is identically zero, then the operators corresponding to the periodic and perturbed equations, respectively, are unitarily equivalent. In some appendices, we also provide the proofs of several basic estimates, e.g. bounds and asymptotics for the relevant m-functions.

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