We develop the -approach to inverse scattering at zero energy in dimensions 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 in the Schrödinger equation from a fixed non-overdetermined (“backscattering” type) restriction of the Faddeev generalized scattering amplitude in the complex domain at zero energy in dimension . For sufficiently small potentials we formulate also a characterization theorem for the aforementioned restriction and a new characterization theorem for the full Faddeev function in the complex domain at zero energy in dimension . 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].
@article{ASNSP_2006_5_5_3_279_0, author = {Novikov, Roman G.}, title = {On non-overdetermined inverse scattering at zero energy in three dimensions}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {279--328}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 5}, number = {3}, year = {2006}, mrnumber = {2274782}, zbl = {1121.35143}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2006_5_5_3_279_0/} }
TY - JOUR AU - Novikov, Roman G. TI - On non-overdetermined inverse scattering at zero energy in three dimensions JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2006 SP - 279 EP - 328 VL - 5 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2006_5_5_3_279_0/ LA - en ID - ASNSP_2006_5_5_3_279_0 ER -
%0 Journal Article %A Novikov, Roman G. %T On non-overdetermined inverse scattering at zero energy in three dimensions %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2006 %P 279-328 %V 5 %N 3 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2006_5_5_3_279_0/ %G en %F ASNSP_2006_5_5_3_279_0
Novikov, Roman G. On non-overdetermined inverse scattering at zero energy in three dimensions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 5 (2006) no. 3, pp. 279-328. http://archive.numdam.org/item/ASNSP_2006_5_5_3_279_0/
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