Dirac Delta Residue?

elfmotat

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).

pwsnafu

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.

elfmotat

Thank you, that was really helpful.