The Paley-Wiener theorem for certain nilpotent Lie groups

We generalize the classical Paley-Wiener theorem to special types of connected, simply connected, nilpotent Lie groups: First we consider nilpotent Lie groups whose Lie algebra admits an ideal which is a polarization for a dense subset of generic linear forms on the Lie algebra. Then we consider nilpotent Lie groups such that the co-adjoint orbits of all the elements of a dense subset of the dual of the Lie algebra g* are flat. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim