  We develop the d-bar -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 Schrodinger
equation from a fixed non-overdetermined ("backscattering type") restriction h
on $\Gamma$ 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
on $\Gamma$ 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].
