convolution properties of distributions

490 Views Asked by At

Let $f,g,h \in D'(R^n)$. How we define the convolution of these functions? I'm trying to show some properties of convolutions such as

  1. $\delta\ast f=f$

  2. $(f\ast g)' = f'\ast g=f\ast g'$

  3. $(f\ast g) \ast h = f \ast (g\ast h)$

but I'm stucked. You can also offer sources about distributions in order to help me to understand.

Thank you.