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Dirac Delta Residue?

  1. Jan 29, 2013 #1
    Does the Dirac delta fuction have a residue? Given the close parallels between the sifting property and Cauchy's integral formula + residue theory, I feel like it should. Unfortunately, I have no idea how they tie together (if they do at all).
  2. jcsd
  3. Jan 29, 2013 #2


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    This is studied in hyperfunction theory, where you write a generalized function as the "difference" between two analytic functions.

    For the record, your intuition is spot on: writing the Dirac as a hyperfunction is a restatement of Cauchy.
  4. Jan 29, 2013 #3
    Thank you, that was really helpful.
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