Re: Fourier transform

In article <paul-47293E.22480519052005@xxxxxxxxxxxxxxx>,
Paul Abbott <paul@xxxxxxxxxxxxxxxxxx> wrote:
>In article
><22111558.1116444456582.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
> billet philippe <philippe.billet@xxxxxxx> wrote:

>> if I choose this formalism for Fourier transform :
>> Fourier(f(t),x)=integral(f(t)*exp(-i*t*x),t,-infinity,infinity).

>In Mathematica, this definition is specified via

> SetOptions[FourierTransform, FourierParameters -> {1, -1}]

>> What are the Fourier transform of this generalized functions :
>> 1/ log(abs(t)),

> FourierTransform[Log[Abs[t]], t, x]

> -2 EulerGamma Pi DiracDelta[x] - Pi/Abs[x]

Can this be right? It is not a tempered distribution.

>> 3/ t^alpha*heaviside(t),
>
>For alpha = n a non-negative integer,
>
> I^n (Pi Derivative[n][DiracDelta][x] - (-1)^n I n!/x^(n + 1))

Similar problem with this when n is odd.

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.

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