  A characterisation of the spaces $\mathcal{G}_K$ and $\mathcal{G}_K'$
introduced in Grothaus et al. (Methods Funct Anal Topol 3(2):46-64, 1997) and
Potthoff and Timpel (Potential Anal 4(6):637-654, 1995) is given. A first
characterisation of these spaces provided in Grothaus et al. (Methods Funct
Anal Topol 3(2):46-64, 1997) uses the concepts of holomorphy on infinite
dimensional spaces. We, instead, give a characterisation in terms of
U-functionals, i.e., classic holomorphic function on the one dimensional field
of complex numbers. We apply our new characterisation to derive new results
concerning a stochastic transport equation and the stochastic heat equation
with multiplicative noise.
