# Convolution theorem

1. Nov 12, 2008

### mhill

1. The problem statement, all variables and given/known data

using the Fourier Transform convolution theorem should be true that

$$i^{m+n}D^{m}\delta (u)D^{n}\delta (u)= A \mathcal F _{u}(\int_{-\infty}^{\infty}dt (t-x)^{m}t^{n} )$$

2. Relevant equations

- Fourier transform convolution theorem (would be valid for distributions ? )

3. The attempt at a solution

i have thought that although the integrals are divergent , the Convolution theorem should hold no matter if we are dealing with distributions (in fact if one of the functions is a distribution but the other is not the convolution theorem holds for example the case f(x)=1 it Fourier transform is a dirac delta but the convolution integral is well defined.