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

Rostyslav O. Hryniv; Yaroslav V. Mykytyuk

doi:10.1088/0266-5611/20/5/006

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

Rostyslav O. Hryniv·Yaroslav V. Mykytyuk

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Abstract

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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Rostyslav O. Hryniv, Yaroslav V. Mykytyuk. 2003-12-09. Half-inverse spectral problems for Sturm--Liouville operators with singular potentials. https://doi.org/10.1088/0266-5611%2F20%2F5%2F006

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