FourierTransform and removable singularities

*To*: mathgroup at smc.vnet.net*Subject*: [mg75295] FourierTransform and removable singularities*From*: Roman <rschmied at gmail.com>*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, 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.