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

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

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 cond...

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Main Authors: Yaroslav Mykytyuk, Nataliia Sushchyk
Format: Article
Language:English
Published: AGH Univeristy of Science and Technology Press 2018-01-01
Series:Opuscula Mathematica
Subjects:
inverse scattering
Schrödinger operator
Banach algebra
Online Access:http://www.opuscula.agh.edu.pl/vol38/5/art/opuscula_math_3832.pdf
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spelling doaj-3a6a5197925242448d5798f4cfa4f9012020-11-25T01:39:15ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742018-01-01385719731https://doi.org/10.7494/OpMath.2018.38.5.7193832Inverse scattering problems for half-line Schrödinger operators and Banach algebrasYaroslav Mykytyuk0Nataliia Sushchyk1Lviv National University, 1 Universytets'ka st. 79602 Lviv, UkraineLviv National University, 1 Universytets'ka st. 79602 Lviv, UkraineThe 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.http://www.opuscula.agh.edu.pl/vol38/5/art/opuscula_math_3832.pdfinverse scatteringSchrödinger operatorBanach algebra
collection DOAJ
language English
format Article
sources DOAJ
author Yaroslav Mykytyuk
Nataliia Sushchyk
spellingShingle Yaroslav Mykytyuk
Nataliia Sushchyk
Inverse scattering problems for half-line Schrödinger operators and Banach algebras
Opuscula Mathematica
inverse scattering
Schrödinger operator
Banach algebra
author_facet Yaroslav Mykytyuk
Nataliia Sushchyk
author_sort Yaroslav Mykytyuk
title Inverse scattering problems for half-line Schrödinger operators and Banach algebras
title_short Inverse scattering problems for half-line Schrödinger operators and Banach algebras
title_full Inverse scattering problems for half-line Schrödinger operators and Banach algebras
title_fullStr Inverse scattering problems for half-line Schrödinger operators and Banach algebras
title_full_unstemmed Inverse scattering problems for half-line Schrödinger operators and Banach algebras
title_sort inverse scattering problems for half-line schrödinger operators and banach algebras
publisher AGH Univeristy of Science and Technology Press
series Opuscula Mathematica
issn 1232-9274
publishDate 2018-01-01
description 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.
topic inverse scattering
Schrödinger operator
Banach algebra
url http://www.opuscula.agh.edu.pl/vol38/5/art/opuscula_math_3832.pdf
work_keys_str_mv AT yaroslavmykytyuk inversescatteringproblemsforhalflineschrodingeroperatorsandbanachalgebras
AT nataliiasushchyk inversescatteringproblemsforhalflineschrodingeroperatorsandbanachalgebras
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