harmonic function
A real or complex-valued function or defined on the vertices of a graph is called harmonic at if its value at is its average value at the neighbours of :
It is called harmonic except on , for some , if it is harmonic at each , and harmonic if it is harmonic at each .
Any harmonic , where is the -dimensional grid, is if below (or above). However, this is not necessarily true on other graphs.
Title | harmonic function |
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Canonical name | HarmonicFunction1 |
Date of creation | 2013-03-22 15:09:27 |
Last modified on | 2013-03-22 15:09:27 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 5 |
Author | mathcam (2727) |
Entry type | Definition |
Classification | msc 05C99 |