Careful, for nilpotence the power doesn't have to be 2. Also you may be confusing it with x^n = 1 (which I'm not sure how to name, 'root of unity' perhaps). Th

Careful, for nilpotence the power doesn't have to be 2. Also you may be confusing it with x^n = 1 (which I'm not sure how to name, 'root of unity' perhaps). This would be the case for the Fourier transform (with n=4). If x^2 = 0 then applying the Fourier transform twice would null your function, which isn't the case.