Characterization of Schwartz multipliers of nilpotent Lie groups

We present a new characterization of Schwartz multipliers on a nilpotent Lie group G with Lie algebra g. We use this characterization to give a sufficient condition for a function phi is an element of C-infinity(g*) to be the Fourier transform of a Schwartz multiplier and we indicate a simpler condition in the case of the Heisenberg group. (C) 1997 Academic Press.