  We study the structure of 2D electronic states in a strong magnetic field in
the presence of a large number of resonant scatterers. For an electron in the
lowest Landau level, we derive the exact density of states by mapping the
problem onto a zero-dimensional field-theoretical model. We demonstrate that
the interplay between resonant and non-resonant scattering leads to a
non-analytic energy dependence of the electron Green function. In particular,
for strong resonant scattering the density of states develops a gap in a finite
energy interval. The shape of the Landau level is shown to be very sensitive to
the distribution of resonant scatterers.
