I would like to compute the convolution of a function with itself, where the function is $f(x) = \frac{\delta(x)}{x}$. When there is a shift in the delta function it is easy to compute, but this one is giving me trouble
I realized that I do not even know what the limit of the function is as x goes to 0. Wolfram said it goes to 0, but they used L'Hospital's rule, which seemed wrong to me since it is of the form $\frac{\infty}{0}$.
Does anyone know how I would go about computing the convolution, or at least how to determine the limit as x goes to 0?