# Linear operator.(2)

1. Jan 23, 2007

### Kevin_spencer2

Let be the linear operator:

$$g(s)=\frac{1}{s} \int_{0}^{\infty}K(\frac{t}{s})df(t)$$

could we invert it?

if we knew the exact expression (or at least approximate) for f(t) and g(t) could we obtain the Kernel K(u) u=s/t ?. thanx i know it's a bit difficult however i would like to hear some opinion, i think a similar expression appears in wikipedia in the article called "Nachbin's theorem' as a generalization to the Borel transform.

http://en.wikipedia.org/wiki/Borel_transform

Last edited: Jan 23, 2007