Inverse scattering problem for Sturm-Liouville operators

zbMATH Open1339.34029arXiv2112.01990MaRDI QIDQ297328

A. A. Asatryan

Publication date: 24 June 2016

Published in: Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences (Search for Journal in Brave)

Abstract: On the space $L^2(mathbbR)$ the Sturm-Liouville operator $L$ with certain behavior of the potential at infinity is considered. It is proved that $L$ is uniquely determined by its scattering data. The recovery of $L$ is reduced to the solving of a certain linear integral equation.

Full work available at URL: https://arxiv.org/abs/2112.01990

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Inverse problems involving ordinary differential equations (34A55) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Related Items (4)

Inverse scattering problems for Sturm-Liouville operators with spectral parameter dependent on boundary conditions ⋮ Description of the scattering data for Sturm-Liouville operators on the half-line ⋮ Title not available (Why is that?) ⋮ Stekloff eigenvalues in inverse scattering

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