modifying standard representation of DiracDelta
- To: mathgroup at smc.vnet.net
- Subject: [mg111350] modifying standard representation of DiracDelta
- From: Benjamin Hell <hell at exoneon.de>
- Date: Wed, 28 Jul 2010 02:55:46 -0400 (EDT)
Hi,
mathematica seems to have the standard representation of the DiracDelta
function set to a*DiracDelta[1+b*f] (with a and b being complex values
and f being the free variable). At least that is the form I get from
using the FourierTransform (for example FourierTransform[Cos[t], t, f,
FourierParameters -> {0, -2 Pi}]) or when just typing in DiracDelta[1/(2
Pi) + f]. The latter Expression is transformed to 2Pi DiracDelta[1 + 2 f
\Pi], which is a valid transformation, but not the one I would like to have.
I would prefer the standard form to be a*DiracDelta[f+b] (with a and b
being complex values and f the free variable). So for me DiracDelta[1/(2
Pi) + f] should stay exactly in that form and DiracDelta[1 +a*f] should
be evaluated to 1/Abs[a]*DiracDelta[1/a + f] which is just another
representation of the same expression. How can I achieve that
respectively how can I implement such a rule?
Thanks in advance.