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Fourier Transform


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



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