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Re: FourierTransform and removable singularities


Limit[FourierTransform[DiracDelta[t - a]*(Sin[
       t]/t), t, w] // FullSimplify, a -> 0]


Roman wrote:
> It seems to me that Mathematica 5.2 is not careful enough when doing
> Fourier transforms of functions with delta functions at removable
> singularities: if you call
>     FourierTransform[DiracDelta[t], t, w]
> you get the right answer,
>     1/Sqrt[2*Pi]
> But if you call something of the sort of
>     FourierTransform[DiracDelta[t]*(Sin[t]/t), t, w]
> which has a removable singularity at the point where the Dirac delta
> function acts, the answer is zero, which is wrong.
> Does anyone know how to resolve this by reformulating the problem? (a
> workaround)
> Cheers!
> Roman.

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