in a paper i have read this:
Consider the Equation PT=S , whereas P is some polynomial of derivation. Then for any smooth function S we can find a smooth function T, s.t. this equation is satisfied.
Then the author says:
" This means that division, in the sense of convolution multiplication, by a polynomial of derivation is always possible".
What does this sentence mean? For polynomials there is no division in general. Therefore the author mean indeed "convolution multiplication". But i don't know what this expression actually means? I know what a convolution of two given functions is. Also what a multiplication is. But not the synthesis like above.