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Complex integral representation of Dirac delta function?

  1. Dec 29, 2009 #1
    We all know that [tex]\frac{1}{2\pi}\int{e^{ik(x-x')}dk=\delta(x-x')[/tex].

    i am working a problem which appears to depend on the statement

    [tex]\int e^{z^*(z-w)}dz^*\propto\delta(z-w)[/tex]

    Does anyone know if this is valid?

    [tex]\delta(z-w)[/tex] is defined in the usual way so that

    [tex]\int{\delta(z-w)f(z)dz}=f(w)[/tex]

    This is a physics problem, though, so the domain of integration is not specified and not clear to me.
     
  2. jcsd
  3. Jan 2, 2010 #2
  4. Jan 3, 2010 #3
    Hi, pellman

    I just saw your thread and remembered reading a similar article on the net. Here it is, I guess it may be helpful:

    http://homepages.physik.uni-muenchen.de/~Winitzki/no_distrib_limit.pdf [Broken]
     
    Last edited by a moderator: May 4, 2017
  5. Jan 4, 2010 #4
    That paper is a very good jumping off point. Thank you!
     
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