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On non-overdetermined inverse scattering at zero energy in three dimensions

Roman G. Novikov — 2006

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We develop the ∂ ¯ -approach to inverse scattering at zero energy in dimensions d ≥ 3 of [Beals, Coifman 1985], [Henkin, Novikov 1987] and [Novikov 2002]. As a result we give, in particular, uniqueness theorem, precise reconstruction procedure, stability estimate and approximate reconstruction for the problem of finding a sufficiently small potential v in the Schrödinger equation from a fixed non-overdetermined (“backscattering” type) restriction h | Γ of the Faddeev generalized scattering amplitude h in the...

Détermination d’un champ de jauge sur ℝ d par sa transformée de Radon non-Abélienne

Roman G. Novikov

Séminaire Équations aux dérivées partielles

Dans cet exposé nous présentons plusieurs résultats récents sur le problème de la détermination d’un champ de jauge sur ℝ d par sa transformée de Radon non-Abélienne le long de droites orientées. Cet exposé est basé en premier lieu sur le travail [R.Novikov, On determination of a gauge field on ℝ d from its non-abelian Radon transform along oriented straight lines, Journal of the Inst. of Math. Jussieu (2002) (4), 559-629].

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