Convolution $f * g$ Assume that $f$ is in $L^1 (\mathbb{R})$ and $g(x)= e^{2iπx}$. Compute $f * g$
I just need a hint and not the entire answer.  How can I compute the convolution when I don't know what $f$ is?

$$(f*g)(x) = \int_{-\infty}^{\infty} f(t) e^{2\pi i(x-t)} dt $$
You can simplify the above as
$$(f*g)(x) = e^{2\pi i x} F(2\pi) $$
Where $F(w) $ is the Fourier transform of $f$
$$ F(w) = \int_{-\infty}^{\infty} f(t) e^{-iwt} dt $$
