# Thread: Division by a polynomial

1. ## Division by a polynomial

Hello,

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.

Regards

2. ## Re: Division by a polynomial

Originally Posted by Sogan
Hello,

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.

Regards
Is this by any chance connected with Laplace Transforms?

(the inverse of a polynomial in the differential operator in this sense still requires initial conditions for uniqueness)

CB