On non-overdetermined inverse scattering at zero energy in three dimensions
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 5 (2006) no. 3, pp. 279-328.

We develop the ¯-approach to inverse scattering at zero energy in dimensions d3 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 complex domain at zero energy in dimension d=3. For sufficiently small potentials v we formulate also a characterization theorem for the aforementioned restriction h| Γ and a new characterization theorem for the full Faddeev function h in the complex domain at zero energy in dimension d=3. We show that the results of the present work have direct applications to the electrical impedance tomography via a reduction given first in [Novikov, 1987, 1988].

Classification: 35R30, 81U40, 86A20
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Novikov, Roman G. On non-overdetermined inverse scattering at zero energy in three dimensions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 5 (2006) no. 3, pp. 279-328. http://archive.numdam.org/item/ASNSP_2006_5_5_3_279_0/

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