Abstract
We start to discuss some aspects of the scattering theory for the Sturm–Liouville operator \(L:\dfrac{1}{y}\left[ -D^2+q\right] \). In particular, we pose and solve the problem of reconstructing the function q when y is fixed and when a set \({\mathcal {S}}\) of scattering data is given. In the meanwhile, several relations concerning the spectral properties of L and the solutions of the related eigenvalue equation are established.
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Notes
The term acoustic is due to the fact that (1) appears in the separation of variables method for solving the wave equation.
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Dedicated to the memory of Russell Johnson.
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Zampogni, L. Some Remarks Concerning the Scattering Theory for the Sturm–Liouville Operator. J Dyn Diff Equat 34, 311–339 (2022). https://doi.org/10.1007/s10884-020-09922-8
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DOI: https://doi.org/10.1007/s10884-020-09922-8