Inverse spectral problems for energy-dependent Sturm-Liouville equations
arXiv:1203.4851 · doi:10.1088/0266-5611/28/8/085008
Abstract
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.
AMS-LaTeX, 28 pages
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- Reconstruction of energy-dependent Sturm-Liouville equations from two spectra
- Asymptotics of eigenvalues and eigenfunctions of energy-dependent Sturm--Liouville equations
- An inverse problem for the matrix quadratic pencil on a finite interval
- On the Lipschitz stability of inverse nodal problem for dirac equation
- Inverse Nodal Problem for P-Laplacian energy-dependent Sturm-Liouville
- Stability of inverse nodal problem for energy-dependent sturm liouville equation