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2003•Inverse ProblemsOpen access

Inverse spectral problems for Sturm Liouville operators with singular potentials

Rostyslav Olegovich Hryniv, Ya. V. Mykytyuk

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Abstract

The inverse spectral problem is solved for the class of Sturm–Liouville operators with singular real-valued potentials from the space W 2 −1 (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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The inverse spectral problem is solved for the class of Sturm–Liouville operators with singular real-valued potentials from the space W 2 −1 (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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Available abstract

The inverse spectral problem is solved for the class of Sturm–Liouville operators with singular real-valued potentials from the space W 2 −1 (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.

Key concepts: Isospectral, Sturm–Liouville theory, Mathematics, Eigenvalues and eigenvectors, Inverse, Inverse problem, Stability (learning theory), Space (punctuation)

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