  The analytic aspects of the operator realization of Wick power series of
infrared singular free fields are considered. Taking advantage of the
holomorphy properties of the two-point correlation function and its Hilbert
majorant in x-space, we solve in a general and model independent way the
problem of finding the adequate test function space on which a given Wick
series is convergent. Substantial attention is paid to the proper formulation
of the spectral condition in case the suitable test functions are entire
analytic in momentum space.
