I have opened a new way that no one obened before in Fourier analysis on non commutative Lie groups, as Heasenberg group, motion group, Galilean group, Jacobi group, Lorentz group, Spacetime (Poincare group) and more as Sl(n,R),Gl+(n,R) in my paper "Fourier transform and Plancherel Formula for Lorentz group", I have proved that there are new groups as R-, O-(n,R) and GL-(n,R)