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Does the Dirac measure still exist on a complex domain?

  1. Jan 2, 2010 #1
    does the Dirac measure still exist with complex variance?

    The Dirac delta function can be rigorously defined as a measure. See

    http://en.wikipedia.org/wiki/Dirac_delta_function#As_a_measure


    For the gaussian form of the Dirac delta function we have,

    [tex]\[
    {\rm{\delta (x - x}}_0 ) = \mathop {\lim }\limits_{\Delta \to 0} \frac{1}{{(2\pi \Delta )^{1/2} }}e^{ - (x - x_0 )^2 /(2\Delta )}
    \]

    [/tex]

    with variance [tex]\Delta[/tex].

    My question is whether the gaussian from of the Dirac delta is still a measure if the variance is complex. Any insight about this would be appreciated.
     
    Last edited: Jan 2, 2010
  2. jcsd
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