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