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.