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FourierTransform and removable singularities

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  • Subject: [mg75295] FourierTransform and removable singularities
  • From: Roman <rschmied at>
  • Date: Tue, 24 Apr 2007 03:24:54 -0400 (EDT)

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,


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


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