Convolution theorem in 3D

Question

Suppose to have a 3-dimensional discrete grid. I would like to convolve it with a 3-dimensional tensor (a 3x3x3 "cube"), applying the convolution theorem. Hence, I should apply a Fourier transform to both the objects and multiply them; but does it work in the 3D case, too? Besides, I do not know how this multiplication works (and even how it is called).

Thank you for your attention.

Answer 1

I discovered that it is possibile to apply the convolution theorem in 3D. There is still the problem of how to compute this product. I am thinking of a tensor contraction...