  Transport through small interacting systems connected to noninteracting leads
is studied based on the Kubo formalism using a Eliashberg theory of the
analytic properties of the vertex part. The transmission probability, by which
the conductance is expressed as $g = (2e^2/h) \int d\epsilon
  (- \partial f / \partial \epsilon) {\cal T}(\epsilon)$, is introduced for
interacting electrons. Here $f(\epsilon)$ is the Fermi function, and the
transmission probability ${\cal T}(\epsilon)$ is defined in terms of a current
vertex or a three-point correlation function. We apply this formulation to a
series of Anderson impurities of size N (=1,2,3,4), and calculate ${\cal
T}(\epsilon)$ using the order $U^2$ self-energy and current vertex which
satisfy a generalized Ward identity. The results show that ${\cal T}(\epsilon)$
has much information about the excitation spectrum: ${\cal T}(\epsilon)$ has
two broad peaks of the upper and lower Hubbard bands in addition to N resonant
peaks which have direct correspondence with the noninteracting spectrum. The
peak structures disappear at high temperatures.
