On the Inverse Resonance Problem for Schrodinger Operators

2009/05/02 by Marco Marletta, Marletta, Marco, Roman Shterenberg +3
Computer Science · Mathematics · #34A55 #34B24 #81U40 #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.0905.0171

openalex publication_date 2009/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider Schrödinger operators on [0,∞) with compactly supported, possibly complex-valued potentials in L¹([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.

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