Re: Multidimensional Residue Theorem

David C. Ullrich <ullrich@xxxxxxxxxxxxxxxx> writes:

On Tue, 01 May 2007 07:43:54 GMT, "Larry Hammick"
<larryhammick@xxxxxxxxx> wrote:

<lhimon@xxxxxxxxx>
Hi All,

Does anyone know if there is a Multidimensional version of Cauchy's
Residue Theorem? Is it orders of magnitude more complicated?
Pointers to references, online or otherwise, would be much
appreciated.
Most of the basic theory of analytic functions goes over to finitely many
variables with no real difficulty; e.g. the basics about power series, and
Cauchy's integral formula. See e.g. "Elementary Theory of Analytic Functions
of One or Several Complex Variables", a textbook by H. Cartan circa 1965.
But what sort of "residue" do you have in mind? A singularity of a function
of several variables is not in general an isolated point.

In fact "never", not just "not in general".

This doesn't, however, prevent there being a theory of multidimensional
residues. (But it *is* "orders of magnitude more complicated".)

Lee Rudolph
.

Relevant Pages

  • Re: Multidimensional Residue Theorem
    ... Residue Theorem? ... Pointers to references, online or otherwise, would be much ... Most of the basic theory of analytic functions goes over to finitely many ...
    (sci.math)
  • Re: Multidimensional Residue Theorem
    ... Residue Theorem? ... Pointers to references, online or otherwise, would be much ... Most of the basic theory of analytic functions goes over to finitely many ...
    (sci.math)
Quantcast