Inverse spectral problems for Sturm Liouville operators with singular potentials

2002/11/17 by Rostyslav Hryniv, R. O. Hryniv, Ya. V. Mykytyuk · 4 citations
Mathematics · Physics and Astronomy · #Numerical methods in inverse problems #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math.SP #msc:34A55 #msc:34B24 #msc:34L05 #msc:34L20

paper · pdf · doi:10.1088/0266-5611/19/3/312

published as Inverse Problems 19 (2003), no. 3, 665-684 · Submitted to Inverse Problems

arxiv created 2002/11/17 · openalex publication_date 2003/04/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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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• Operator-differential expressions: regularization and completeness of the root functions
• A generalized Birman-Schwinger principle and applications to one-dimensional Schrödinger operators with distributional potentials

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