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what is product of delta function with itself ?

why $2$ or more dirac delta distributions can not be multiplied ?? i mean to define a coherent product of

$d(x)$ x $d'(x)$ with $d(x)$ being the dirac delta derivative

using the convolution theorem plus regularization i think we could.

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1 Answer 1

If you mean $\delta (x) ^2$, it can be defined well as a very large positive number (infinity). Some people are shy of infinities and call the product "undetermined". It is undetermined only in one sense: it is larger than any finite number but it is not zero or any other finite number usually "ascribed" to the product in renormalizations.

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