  The single channel Anderson impurity model is a standard model for the
description of magnetic impurities in metallic systems. Usually, the bandwidth
represents the largest energy scale of the problem. In this paper, we analyze
the limit of a narrow band, which is relevant for the Mott-Hubbard transition
in infinite dimensions. For the symmetric model we discuss two different
effects: i) The impurity contribution to the density of states at the Fermi
surface always turns out to be negative in such systems. This leads to a new
crossover in the thermodynamic quantities that we investigate using the
numerical renormalization group. ii) Using the Lanczos method, we calculate the
impurity spectral function and demonstrate the breakdown of the skeleton
expansion on an intermediate energy scale. Luttinger's theorem, as an example
of the local Fermi liquid property of the model, is shown to still be valid.
