How can you derive the regularization of a product with a delta function?

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SUMMARY

The discussion centers on the regularization of the product involving the delta function, specifically the expression sgn(x)^2 δ(x) = δ(x)/3. The user sought clarification on deriving this relationship, indicating a successful resolution to their inquiry. This highlights the application of distribution theory in mathematical physics, particularly in the context of regularization techniques for delta functions.

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  • Familiarity with delta functions and their properties
  • Knowledge of the sign function (sgn)
  • Basic concepts of regularization techniques in mathematics
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atrahasis
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Hi,

I was wondering about something a friend told me. He said that we can regularize this product in this form

[itex]sgn(x)^2 \delta(x)=\frac{\delta(x)}{3}[/itex]

Any guess on how to derive it

Thanks.
 
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Ok, finally I have it.
 

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