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How can use the Colombeau generalized function method to evaluate the product of distributions $ \delta (x) \times \delta (x) $ or $ \delta ^{n} (x) \times \delta ^{m} (x) $ (derivatives of dirac delta) or the product $ \delta (x) \times P(1/x) $?

How could I do it?

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one should be a bit careful: while there is a surjective map from the space of Colombeau functions to the space of distributions, but it is not injective. There is no natural inverse map. You need to say explicitly what you mean by $\delta$ as a Colombeau function - different choices give different results. – user8268 Jul 18 '12 at 11:39

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