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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) andPotthoff and Timpel (Potential Anal 4(6):637-654, 1995) is given. A firstcharacterisation of these spaces provided in Grothaus et al. (Methods FunctAnal Topol 3(2):46-64, 1997) uses the concepts of holomorphy on infinitedimensional spaces. We, instead, give a characterisation in terms ofU-functionals, i.e., classic holomorphic function on the one dimensional fieldof complex numbers. We apply our new characterisation to derive new resultsconcerning a stochastic transport equation and the stochastic heat equationwith multiplicative noise.

An improved characterisation of regular generalised functions of white noise and an application to singular SPDEs