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Re: FoourierTransform of a function defined in sections

• To: mathgroup at smc.vnet.net
• Subject: [mg70195] Re: [mg70176] FoourierTransform of a function defined in sections
• From: Sseziwa Mukasa <mukasa at jeol.com>
• Date: Sat, 7 Oct 2006 07:07:22 -0400 (EDT)
• References: <200610060559.BAA15565@smc.vnet.net>

On Oct 6, 2006, at 1:59 AM, Eckhard Schlemm wrote:

> Hello,
>
> I want Mathematica to calculate the FourierTransform of a function  
> which is
> defined by Sin[x]^2 for Abs[x]<PI and zero else. I tried and  
> defined the
> function g as follows:
>
> g[x_]:=If[Abs[x]>PI,0,Sin[x]^2];
>
> That works fine. But if I have mathematica try to determine the
> FourierTransform by
>
> FourierTransform[g[x],x,p]
>
> I always get the error that the recursion limit and the iteration  
> limit were
> exceeded...
>
> what am I'm doing wrong?

I don't know what is going wrong with your expression but I would use  
UnitStep to define your function.  Then

FourierTransform[Sin[x]^2 UnitStep[Pi^2-x^2],x,p]

gives you your expected result.

Regards,

Sseziwa

• References:
  • FoourierTransform of a function defined in sections
    • From: "Eckhard Schlemm" <e.schlemm@hotmail.de>