I am physicist so sorry for being not very formal.
I calculate now a lot of stuff with Laplace transform: so have some functions $f_1(t),f_2(t)$ calculate $\mathcal{L}(f_i(t))=F_i(u)$, calculate some functional $G[F_1(u),F_2(u)]$, then the corresponding inverse Laplace function $g(t)$.
My problem is: I have never paid any attention on the restrictions Laplace transforms of some functions come with (mostly $\Re(u)>0$, but depending on function it can be different).
Is that any problem for the calculations?