Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Dirac delta function on the complex plane?

  1. Apr 16, 2003 #1

    ∫ ez*(z - z0)f(z) dz*dz

    is proportional to f(z0) much in the same way that

    (1/2π)∫ eiy(x - x0)f(x) dxdy
    = ∫ δ(x - x0)f(x) dx
    = f(x0)

    Is this true? Could someone help convince me of it, or point me to a text?

    I would say that even if true, it would be incorrect to say that

    ∫ ez*(z - z0)dz* = δ(z - z0)

    because the integration over dz and dz* cannot be done independently in the same way that a surface integral over dxdy in the plane can (sometimes) be separated into independent integrations over x and y. Or can it?
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?