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The inverse problem for a spectral asymmetry function of the Schrodinger operator on a finite interval

Brown, B. Malcolm, Schmidt, Karl Michael, Shipman, Stephen P., Wood, Ian (2021) The inverse problem for a spectral asymmetry function of the Schrodinger operator on a finite interval. Mathematika, 67 (4). pp. 788-806. ISSN 0025-5793. E-ISSN 2041-7942. (doi:10.1112/mtk.12105) (KAR id:89258)

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Official URL:
https://doi.org/10.1112/mtk.12105

Abstract

For the Schroedinger equation \(−d^2u/dx^2 + q(x)u = λu\) on a finite \(x\)-interval, there is defined an “asymmetry function” \(a(λ; q)\), which is entire of order 1/2 and type 1 in \(λ\). Our main result identifies the classes of square-integrable potentials \(q(x)\) that possess a common asymmetry function \(a(λ)\). For any given \(a(λ)\), there is one potential for each Dirichlet spectral sequence.

Item Type: Article
DOI/Identification number: 10.1112/mtk.12105
Uncontrolled keywords: spectral theory; Schrodinger operator; inverse spectral problem; entire function; asymmetry function
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Ian Wood
Date Deposited: 14 Jul 2021 09:15 UTC
Last Modified: 12 Aug 2021 13:22 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/89258 (The current URI for this page, for reference purposes)
Wood, Ian: https://orcid.org/0000-0001-7181-7075
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