These work:
In[363]:= Integrate[+I*DiracDelta[x], {x, -Infinity, +Infinity}]
Out[363]= I
In[364]:= Integrate[-I*DiracDelta[x], {x, -Infinity, +Infinity}]
Out[364]= -I
But Mathematica doesn't evaluate this:
In[367]:= Integrate[
Conjugate[+I*DiracDelta[x]], {x, -Infinity, +Infinity}]
More generally, I need a function that does something like this:
testFunction2[signal_] :=
Integrate[
signal[x] + Conjugate[signal[x]], {x, -Infinity, +Infinity}]
But my naive implementation fails to evaluate this to zero:
In[366]:= testFunction2[(I*DiracDelta[#]) &]
Is there a way to implement this so that Mathematica will recognize that the conjugate of (the product of a complex-number and DiracDelta) equals the product of (the conjugate of the complex-number) and DiracDelta? This axiom is true in conventional theories of generalized functions, no?
