, Volume 295, Issue 2, pp 465-484

On the Inverse Resonance Problem for Schrödinger Operators

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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.

Communicated by B. Simon