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February  2007, 1(1): 217-224. doi: 10.3934/ipi.2007.1.217

Inverse scattering at a fixed energy for long-range potentials

Ricardo Weder 1, and  Dimitri Yafaev 2,

1. 

Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apartado Postal 20-726, México DF 01000, United States
2. 

IRMAR, Université de Rennes I., Campus de Beaulieu, 35042 Rennes, Cedex, France

Received  September 2006 Published  January 2007

In this paper we consider the inverse scattering problem at a fixed energy for the Schrödinger equation with a long-range potential in $R^d, d\geq 3$. We prove that the long-range part can be uniquely reconstructed from the leading forward singularity of the scattering amplitude at some positive energy.
Keywords: fixed energy., inverse scattering, long-range potentials.
Mathematics Subject Classification: Primary: 81U40, 35P25, 35Q40, 35R3.
Citation: Ricardo Weder, Dimitri Yafaev. Inverse scattering at a fixed energy for long-range potentials. Inverse Problems and Imaging, 2007, 1 (1) : 217-224. doi: 10.3934/ipi.2007.1.217
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