Fourier transforms are not commutative or distributive

Problem with yesterday's work:

A*B = IFT(FT(A)*FT(B))
A*B - A*C != IFT(FT(A)*(FT(B)-FT(C)))

If instead of yesterday's "bandpass filter" you use the convolution - convolution 'filter', the agreement in real space and most of fourier space is much better:

though map20 clearly reproduces some structures better (higher) but is overall less powerful than the filtered map.