Communications in Mathematical Physics

, Volume 295, Issue 2, pp 465–484

On the Inverse Resonance Problem for Schrödinger Operators

Article

DOI: 10.1007/s00220-009-0928-8

Cite this article as:
Marlettta, M., Shterenberg, R. & Weikard, R. Commun. Math. Phys. (2010) 295: 465. doi:10.1007/s00220-009-0928-8

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.

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Marco Marlettta
    • 1
  • Roman Shterenberg
    • 2
  • Rudi Weikard
    • 2
  1. 1.School of MathematicsCardiff UniversityCardiffWales
  2. 2.Department of MathematicsUniversity of Alabama at BirminghamBirminghamUSA