I am studying convolution through an open source textbook I found and am confused on how I should approach convolution with two complex exponentials.
Provided $x(t) = e^{-j \omega t}*u(t)$, and $h(t) = e^{j \omega t}*u(t)$. Time reversing and shifting h(t), I get a convolution integral of the form (Adjusting the limits due to our step functions we can set the lower bound to be 0):
$$ \int_{0}^{\infty} e^{-j \omega \tau}e^{-j \omega (t-\tau)}d\tau $$
However, the integrand reduces to $ e^{-j*\omega*t} $, so integrating brings $\tau$ as a coefficient and we get an infinite result for the integral. Am I going wrong somewhere? I don't feel like the convolution should be divergent for these two functions.