Opuscula Math. 39, no. 4 (2019), 557-576

Opuscula Mathematica

Description of the scattering data for Sturm-Liouville operators on the half-line

Yaroslav Mykytyuk
Nataliia Sushchyk

Abstract. We describe the set of the scattering data for self-adjoint Sturm-Liouville operators on the half-line with potentials belonging to \(L_1(\mathbb{R}_+,\rho(x)\,\text{d} x)\), where \(\rho:\mathbb{R}_+\to\mathbb{R}_+\) is a monotonically nondecreasing function from some family \(\mathscr{R}\). In particular, \(\mathscr{R}\) includes the functions \(\rho(x)=(1+x)^{\alpha}\) with \(\alpha\geq 1\).

Keywords: inverse scattering, Schrödinger operator, Banach algebra.

Mathematics Subject Classification: 34L25, 34L40, 47L10, 81U40.

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  • Communicated by P.A. Cojuhari.
  • Received: 2019-01-26.
  • Revised: 2019-03-19.
  • Accepted: 2019-03-20.
  • Published online: 2019-05-23.
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Cite this article as:
Yaroslav Mykytyuk, Nataliia Sushchyk, Description of the scattering data for Sturm-Liouville operators on the half-line, Opuscula Math. 39, no. 4 (2019), 557-576, https://doi.org/10.7494/OpMath.2019.39.4.557

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