I want to calculate the convolution of a function and its inverse,
$$f(t) * f^{-1}(t)$$
e.g. $f(t)=1/(t-2i)$
I've heard that the answer can be a delta function. What requirements are necessary for $f(t)$ to give a $\delta$-function?
Edit: I should add that $f^{-1}(t)=1/f(t)$ in the above equation.