Inverse spectral problems for Sturm-Liouville operators with singular potentials

Details Inverse spectral problems for Sturm-Liouville operators with singular potentials Inverse spectral problems for Sturm-Liouville operators with singular potentials

2002-11-17

arxiv.org/abs/math/0211247v1

Inverse Problems 19 (2003), no. 3, 665-684

Mathematics

Spectral Theory

Submitted to Inverse Problems

Scientific paper

10.1088/0266-5611/19/3/312

The inverse spectral problem is solved for the class of Sturm-Liouville operators with singular real-valued potentials from the space $W^{-1}_2(0,1)$. The potential is recovered via the eigenvalues and the corresponding norming constants. The reconstruction algorithm is presented and its stability proved. Also, the set of all possible spectral data is explicitly described and the isospectral sets are characterized.

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