Inverse spectral problems for energy-dependent Sturm-Liouville equations

Details Inverse spectral problems for energy-dependent Sturm-Liouville equations Inverse spectral problems for energy-dependent Sturm-Liouville equations

2012-03-21

arxiv.org/abs/1203.4851v1

Mathematics

Spectral Theory

AMS-LaTeX, 28 pages

Scientific paper

We study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from their Dirichlet spectra and sequences of the norming constants. For the class of problems under consideration, we give a complete description of the corresponding spectral data, suggest a reconstruction algorithm, and establish uniqueness of reconstruction. The approach is based on connection between spectral problems for energy-dependent Sturm-Liouville equations and for Dirac operators of special form.

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