Abstract
LetG be a nilpotent Lie group. The adapted nilpotent Fourier transformℰ was introduced by D. Arnal and J. C. Cortet,ℰ:L(G) →C ∞(V,L(∝2d )), whereL(G) is the Schwartz space ofG andV × ∝2k is aG-invariant Zariski open set ing * the dual of the Lie algebra ofG. We prove the surjectivity of this transformation, which allows us to extend it to distribution spaces.
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