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Re: Bug in FourierTransform?

• To: mathgroup at smc.vnet.net
• Subject: [mg122679] Re: Bug in FourierTransform?
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Sat, 5 Nov 2011 04:49:05 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201111041101.GAA29219@smc.vnet.net>

On 11/04/2011 06:01 AM, Rui wrote:
> Is there anything about Slot that I don't know that explains this behaviour?
>
> FourierTransform[Sin[t], t, #]
> Out= 0
>
> Only by changing # to p I get the correct result
> FourierTransform[Sin[t], t, p]
> Out= (-I)*Pi*DiracDelta[1 - 2*p*Pi] + I*Pi*DiracDelta[1 + 2*p*Pi]
>
> It happens with Cos too, but not for imaginary exopnentials or other simpel functions like UnitBox
> Bug?
>

It's a limitation-- I would definitely not regard it as a bug. It arises 
from the fact that some parts of FourierTransform use pure functions in 
their implementation. The Slot[] argument can, in such cases, be 
"captured" in the scope of a pure function, thus completely changing the 
computation.

Daniel Lichtblau
Wolfram Research

• References:
  • Bug in FourierTransform?
    • From: Rui <rui.rojo@gmail.com>