Abstract
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.
Original language | English (US) |
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Pages (from-to) | 207-225 |
Number of pages | 19 |
Journal | Journal of Computational and Applied Mathematics |
Volume | 208 |
Issue number | 1 SPEC. ISS. |
DOIs | |
State | Published - Nov 1 2007 |
Externally published | Yes |
Keywords
- Scattering coefficients
- Sturm-Liouville equations
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics