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Let $g:\mathbb{R}\to \mathbb{R}$ be a given differentiable function of exponential decay on both sides. Now let us be given a function $f:\mathbb{R}\to \mathbb{R}$, also of exponential decay, if you ...

Consider the following formula which defines a piece-wise function which I believe corresponds to a series representation for the Dirac delta function $\delta(x)$. The parameter $f$ is the evaluation ...