Opuscula Math. 38, no. 5 (2018), 719-731
https://doi.org/10.7494/OpMath.2018.38.5.719

 
Opuscula Mathematica

Inverse scattering problems for half-line Schrödinger operators and Banach algebras

Yaroslav Mykytyuk
Nataliia Sushchyk

Abstract. The inverse scattering problem for half-line Schrödinger operators with potentials from the Marchenko class is shown to be closely related to some Banach algebra of functions on the line. In particular, it is proved that the topological conditions in the Marchenko theorem can be replaced by the condition that the scattering function should belong to this Banach algebra.

Keywords: inverse scattering, Schrödinger operator, Banach algebra.

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

Full text (pdf)

  1. V.A. Marchenko, Sturm-Liouville Operators and their Applications, Kiev: Naukova Dumka, 1977 [in Russian]; Engl. transl., Basel. Birkhäuser, 1986.
  • Yaroslav Mykytyuk
  • Lviv National University, 1 Universytets'ka st. 79602 Lviv, Ukraine
  • Nataliia Sushchyk
  • Lviv National University, 1 Universytets'ka st. 79602 Lviv, Ukraine
  • Communicated by Alexander Gomilko.
  • Received: 2017-11-03.
  • Accepted: 2018-02-04.
  • Published online: 2018-06-12.
Opuscula Mathematica - cover

Cite this article as:
Yaroslav Mykytyuk, Nataliia Sushchyk, Inverse scattering problems for half-line Schrödinger operators and Banach algebras, Opuscula Math. 38, no. 5 (2018), 719-731, https://doi.org/10.7494/OpMath.2018.38.5.719

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