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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.2012-07-18

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