Half-inverse spectral problems for Sturm--Liouville operators with singular potentials

Details Half-inverse spectral problems for Sturm--Liouville operators with singular potentials Half-inverse spectral problems for Sturm--Liouville operators with singular potentials

2003-12-09

arxiv.org/abs/math/0312184v1

Inverse Problems 20 (2004), no. 5, 1423 - 1444.

Mathematics

Spectral Theory

21 pages

Scientific paper

10.1088/0266-5611/20/5/006

Half-inverse spectral problem for a Sturm--Liouville operator consists in reconstruction of this operator by its spectrum and half of the potential. We give the necessary and sufficient conditions for solvability of the half-inverse spectral problem for the class of Sturm--Liouville operators with singular potentials from the space $W^{-1}_2(0,1)$ and provide the reconstruction algorithm.

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