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FourierTransform gives strange result

  • To: mathgroup at smc.vnet.net
  • Subject: [mg9731] FourierTransform gives strange result
  • From: Pedro A Santos <pasantos at math.ist.utl.pt>
  • Date: Tue, 25 Nov 1997 00:06:31 -0500
  • Organization: I.S.T. - Portugal
  • Sender: owner-wri-mathgroup at wolfram.com

Hello,

Trying the following in Mathematica 3.0 gives

In[1]:=<<Calculus`FourierTransform`
$FourierOverallConstant = 1
$FourierFrequencyConstant =-2*Pi

In[2]:=FourierTransform[UnitStep[x]*Exp[I*k0*x*Cos[\[Theta]]],x,y, 
  Assumptions->{Im[k0]>0,Re[k0] > 0}]

Out[2]:=-(I/(2*Pi*y - k0*Cos[\[Theta]])) + 
  1/2*DiracDelta[y - (k0*Cos[\[Theta]])/(2*Pi)]

and the DirecDelta part seems not to be correct. If one specifies k0:

In[3]:= k0=10^6+10^(-6)*I

and repeat the FourierTransform, then Mathematica returns the correct
result(without the DiracDelta). Does anyone know why this strange
result appears?

Thanks

Pedro Santos


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