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.
- 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.
