Fourier Transform

*To*: mathgroup at smc.vnet.net*Subject*: [mg13689] Fourier Transform*From*: Edward Neuman <edneuman at siu.edu>*Date*: Sat, 15 Aug 1998 04:39:20 -0400*Organization*: SIUC*Sender*: owner-wri-mathgroup at wolfram.com

Let f(x) = 1/x. If f is regarded as the generalized function, then its Fourier transform is: -Pi*I*Sign[t] (see, e.g., G.B. Folland, "Fourier Analysis and Its Applications," p. 337). Using Mathematica 3.0 we get: In[1]:= << "Calculus`FourierTransform`" In[2]:= FourierTransform[1/x, x, t] Out[2]= 2*I*Pi*(-(1/2) + UnitStep[t, ZeroValue -> 1/2]). This agrees with the above result only if t = 0. Bug? Edward Neuman