Paley-Wiener properties for spaces of power series expansions

We extend Paley-Wiener results in the Bargmann setting deduced earlier by the author together with E. Nabizadeh and C. Pfeuffer to larger class of power series expansions. At the same time we deduce characterisations of all Pilipovi{'c} spaces and their distributions (and not only of low orders as in the earlier work).