Example in a Rectangular Lattice
Suppose we wish to determine all
eigenfunctions of the Laplacian that are invariant under an action of pmg on the plane. This group is a good place to
start because it's neither too simple nor too complicated.
The first step would be to find eigenfunctions that are invariant with
respect to horizontal and vertical translations . Then we would determine which of these are also invariant
under half-turns , and finally what conditions
are required for those to be invariant under the mirror reflections that are
in the group . This will provide us with a
recipe for generating functions invariant under pmg
Communications in Visual Mathematics, vol 1, no 1, August 1998.
Copyright © 1998,
The Mathematical Association of America.
All rights reserved.
Created: 12 Aug 1998 ---
Last modified: Sep 30, 2003 9:26:46 AM
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