  Propagators approximated by a meromorphic functions with complex conjugated
poles are widely used to model infrared behavior of QCD Green's functions. In
this paper, analytical solutions for two point correlator made out of functions
with complex conjugated poles or branch points have been obtained in the
Minkowski space for the first time. As a special case the Gribov propagator has
been considered as well. The result is different from the naive analytical
continuation of the correlator primarily defined in the Euclidean space. It is
free of ultraviolet divergences, and instead of Lehmann it rather satisfies
Gribov integral representation.
