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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.

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