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There's a lot of research being done in 3D shape analysis when it comes to PDE methods. Recently I've been reading quite a bit of literature on this subject and recent trends in this subject propose different basis all the time.

The common way to define such a basis is to define an operator or an energy function whose minimization leads to an eigenvalue problem.

In some situations equations of the form

$$ Tx = \lambda x $$

Lead to an orthonormal basis, classic example of this is the well known Spherical Harmonics. However I thought I had is whether or not people have used different basis from Spherical Harmonics to represent light.

Can anyone provide me examples or some literature to look into?

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