nick11
Jun6-11, 10:46 AM
Hi all,
I'm asking myself how to best numerically count the zeros of a, say, holomorphic function $\psi:\Omega\to\C$ where $\Omega$ is open and bounded in $\R^d$.
So far I only considered $d=2$ and just counted the phase jumps in $\arg\psi$ around the boundary of the domain, but that doesn't easily translate into $d=3$.
I've mostly been looking at Cauchy's integral theorem, the residual theorem and such so far.
Any ideas?
I'm asking myself how to best numerically count the zeros of a, say, holomorphic function $\psi:\Omega\to\C$ where $\Omega$ is open and bounded in $\R^d$.
So far I only considered $d=2$ and just counted the phase jumps in $\arg\psi$ around the boundary of the domain, but that doesn't easily translate into $d=3$.
I've mostly been looking at Cauchy's integral theorem, the residual theorem and such so far.
Any ideas?