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[✓] Simplify Conjugate[DiracDelta[x]]?

GROUPS:

Assuming x is Real, how to get Mathematica to recognize the truth of this equation?

In[513]:= FullSimplify[Conjugate[DiracDelta[x]] == DiracDelta[x], 
 x \[Element] Reals]

Out[513]= Conjugate[DiracDelta[x]] == DiracDelta[x]
POSTED BY: Joe Donaldson
Answer
19 days ago

Try ComplexExpand.

POSTED BY: Chris P
Answer
19 days ago

Thanks.

POSTED BY: Joe Donaldson
Answer
19 days ago

When x=0, DiracDelta[x] is not considered a number:

In[8]:= DiracDelta[0] // NumberQ

Out[8]= False

Mathematica simplifies as you expect when x!=0:

Simplify[Conjugate[DiracDelta[x]] == DiracDelta[x], 
 x \[Element] Reals && x != 0]
POSTED BY: Gianluca Gorni
Answer
19 days ago

Thank you. That is helpful.

POSTED BY: Joe Donaldson
Answer
18 days ago

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