Re: fourier transform of 1/|x|

Indeed, I meant a one-dimensional FT.

Gradshteyn/Ryzhik (4th ed.) list the FT of 1/|x| as 1/|k| in 17.23.
I believe it is correct in some sense.

Mathematica gives
FourierTransform[1/Abs[x],x,k] = (-2 EulerGamma - 2 Log[Abs[k]])/Sqrt
[2 Pi]

I'm well aware that \int\cos(kx)/|x| diverges around x=0, but I
suspect there is a way to restrict the support of the function and
define a meaningful FT.

Thanks for any help.
.

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