Dirac Delta Residue?


by elfmotat
Tags: delta, dirac, residue
elfmotat
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#1
Jan29-13, 01:02 AM
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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).
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pwsnafu
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Jan29-13, 06:07 AM
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Quote Quote by elfmotat View Post
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).
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
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Jan29-13, 08:07 AM
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Thank you, that was really helpful.


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