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In this paer we will study the wellposed of the inital value problem associated to the homogeneous left invariant differential operator on the Heisenberg group by the method of group Forier anasis L=(-1)^k/2^k ∑j=1^1 aj(Zj^k Zj^-k+Zj^-kZj^k)+(-i)^3k rS^