The jump from spherical harmonics to eigenfunctions on a general mesh, and the specific example mesh chosen, might be the finest mathematical joke I've seen this decade.
>If you’re alarmed by the fact that the set of all real functions does not form a HILBERT SPACE, you’re probably not in the target audience of this post."
If you're wondering what a Hilbert space, know that you're in good company.
> Dr. von Neumann, ich möchte gerne wissen, was ist denn eigentlich ein Hilbertscher Raum?
(Dr. von Neumann, I'd would really like to know, just what exactly is a Hilbert space?)
Asked to John von Neumann to David Hilbert at a lecture.
I'd like to add, as a physicist by training, that anything can be a Hilbert space if you wish hard enough. You can even use results about countable vector spaces if you need them!
It's quietly reversing the traditional "We approximate the cow to be a sphere" and showing how the spherical math can, in fact, be generalized to solutions on the cow.
