Inverse spectral problems for Sturm-Liouville operators with singular potentials, IV. Potentials in the Sobolev space scale

Details Inverse spectral problems for Sturm-Liouville operators with singular potentials, IV. Potentials in the Sobolev space scale Inverse spectral problems for Sturm-Liouville operators with singular potentials, IV. Potentials in the Sobolev space scale

2004-06-11

arxiv.org/abs/math/0406238v1

Proceedings of the Edinburgh Mathematical Society 49 (2006), 309--329

Mathematics

Functional Analysis

16 pages

Scientific paper

10.1017/S0013091504000859

We solve the inverse spectral problems for the class of Sturm--Liouville
operators with singular real-valued potentials from the Sobolev space
W^{s-1}_2(0,1), s\in[0,1]. The potential is recovered from two spectra or from
the spectrum and norming constants. Necessary and sufficient conditions on the
spectral data to correspond to the potential in W^{s-1}_2(0,1) are established.

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