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Re: Hilbert transform bug in 7.0.3?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg100930] Re: Hilbert transform bug in 7.0.3?
  • From: Nacho <ncc1701zzz at gmail.com>
  • Date: Thu, 18 Jun 2009 06:17:54 -0400 (EDT)
  • References: <h19i5r$p4g$1@smc.vnet.net> <h1a9pf$7vv$1@smc.vnet.net>

Hi Daniel.

You are right, without PrincipalValues, it works fine. I took the
definition from Mathworld directly, and it seems it works with the
PrincipalValues->True in previous versions.

Thanks.

Regards.



On Jun 17, 10:33 am, dh <d... at metrohm.com> wrote:
> Hi Nacho,
>
> your problem comes from the fact that you are using PrincipalValue ->
>
> True together with DiracDelta. Consider the simplest case:
>
> Integrate[DiracDelta[x], {x, -Infinity, Infinity}]
>
> Integrate[DiracDelta[x], {x, -Infinity, Infinity},PrincipalValue -> True]
>
> The first integral gives 1 in agreement with the definition of
>
> DiracDelta. The second integral is actually a limit of two integrals.
>
> One from -Infinity to epsilon. The second from epsilon to Infinity. For
>
> epsilon > 0 both integrals are zero. Therefore, the limit is also zero.
>
> Daniel
>


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