On inverse scattering at a fixed energy for potentials with a regular behaviour at infinity

doi:10.1088/0266-5611/21/6/009

On inverse scattering at a fixed energy for potentials with a regular behaviour at infinity^*

Ricardo Weder et al 2005 Inverse Problems 21 1937-1952 doi: 10.1088/0266-5611/21/6/009

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Ricardo Weder¹ and Dimitri Yafaev²
¹ Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apartado Postal 20-726, México 01000, DF, Mexico
² IRMAR, Université de Rennes I, Campus de Beaulieu, 35042 Rennes Cedex, France
E-mail: weder@servidor.unam.mx and yafaev@univ-rennes1.fr

Abstract. We study the inverse scattering problem for electric potentials and magnetic fields in ${\bb R}^d, d\geq 3$ , that are asymptotic sums of homogeneous terms at infinity. The main result is that all these terms can be uniquely reconstructed from the singularities in the forward direction of the scattering amplitude at some positive energy.

^* Research partially supported by Universidad Nacional Autónoma de México under project PAPIIT-DGAPA IN 105799, by CONACYT under project P42553F and by the European Group of Research SPECT.

Print publication: Issue 6 (December 2005)
Received 9 August 2005, in final form 23 September 2005
Published 14 October 2005

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On inverse scattering at a fixed energy for potentials with a regular behaviour at infinity^*

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On inverse scattering at a fixed energy for potentials with a regular behaviour at infinity*

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On inverse scattering at a fixed energy for potentials with a regular behaviour at infinity^*