On the inverse resonance problem for Schrödinger operators

Marletta, Marco ORCID: https://orcid.org/0000-0003-1546-4046, Shterenberg, Roman and Weikard, Rudi 2010. On the inverse resonance problem for Schrödinger operators. Communications in Mathematical Physics 295 (2) , pp. 465-484. 10.1007/s00220-009-0928-8

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Abstract

We consider Schrödinger operators on [0, ∞) with compactly supported, possibly complex-valued potentials in L 1([0, ∞)). It is known (at least in the case of a real-valued potential) that the location of eigenvalues and resonances determines the potential uniquely. From the physical point of view one expects that large resonances are increasingly insignificant for the reconstruction of the potential from the data. In this paper we prove the validity of this statement, i.e., we show conditional stability for finite data. As a by-product we also obtain a uniqueness result for the inverse resonance problem for complex-valued potentials.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Springer
ISSN:	0010-3616
Last Modified:	18 Oct 2022 12:52
URI:	https://orca.cardiff.ac.uk/id/eprint/11464

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