We have indefinite integral of the product of two functions:
$\int f(t) \cdot g(t) dt$
given that $t∈R$, and functions $f(t),g(t)$ defined in the interval $[0,+\infty)$
Is there a transformation that allow write this integral as a convolution, i.e.:
$\int f(t) \cdot g(t) dt = \int_{0}^{t} h(s) ds$
where $h(s)$ - new function of integral transform.
The question is, how to find the $h(s)$?
This is necessary to transform a differential equation into an integral one and solve it using the Laplace transform.
I would be glad to any advice and help.