I have to find the convolution product $e^t h(t) * h(t-1)$ using the property $\Phi(f * g) = \Phi(f)_{(w)} \Phi(g)_{(w)}$ where $\Phi$ is used to denote Fourier's transform and $h(t)$ is Heaviside function.
I started by transforming both sides to use the mentioned property, so I tried to transform $\Phi(e^{t}h(t))$ but I couldn't go further beacuse the integral seems to have no solution.
Is possible that the excercise has a typo or the transform is resolvable? I also would like to mention that WolframAlpha (software that I use only to check my answer) displays that it has no solution.