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Use Convolve with a Dirac Delta function?

Posted 13 days ago
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In Wolfram Mathematica 11.3 Convolve[1, xDiracDelta[x], x, y] gives no result. But the equivalent function Integrate[xDiracDelta[x], {x, -[Infinity], [Infinity]}] gives the correct result which is 0.

2 Replies
Posted 13 days ago

Try setting the GenerateConditions option to True to find a conditional expression where the results are valid.

Convolve[x DiracDelta[x], g[x] , x, y, 
 GenerateConditions -> True] (* 0 *)
Convolve[g[x], x DiracDelta[x], x, y, 
 GenerateConditions -> True] (* 0 *)

It appears that the answer is "0" for all conditions and for any function, g[x].

Posted 13 days ago

Yes, with this option it works properly.

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