Tag Archives: laplace transform

Statement: Let $L_f(t) = \int_0^\infty f(x)e^{-tx} dx$. Then if $f(x) = o(e^{ax})$ for some $a > 0$, $L_f = L_g$ implies $f = g$. Proof: By linearity of the integral, this is equivalent to showing $L_f = 0$ implies $f = … Continue reading →