  We study analytic structure of the Green's function (GF) for the exactly
solvable Fano-Anderson model. We analyze the GF poles, branch points and
Riemann surface, and show how the Fermi's Golden Rule, valid in perturbative
regime for not to large time, appears in this context. The knowledge of
analytic structure of the GF in frequency representation opens opportunities
for obtaining formulas for the GF in time representation alternative to the
standard one using the spectral density.
