What is the Correct Approach to Solving This 3D Fourier Transform Problem?

[Sina]

Homework Statement

What is the function f(r) s.t

$$int {d³r.f(r).e^-iw.r= 1/w²}$$

where w = (k_x,k_y,k_z)

Homework Equations

None

The Attempt at a Solution

I tried to directly take Fourier transform of 1/w² as $$\int{ d³r.1/w².e^iw.r}$$. I started integrating dk_x bu calculus of residues, calling the denominator k_x² + c² and evaluating residues at k_x = ic with a semi circle in the lower plane etc. However the integral I get from here is with roots and strange exponential terms so I stopped here. So I am asking for a line of approach should I be working in polar coordinates to solve this questions. And also what are some general methods approach n-dimensional Fourier transformations.Thanks

 

[vela]

Try polar coordinates instead. I haven't worked it out, but that's what I'd try.