As I understand it, the Spherical harmonics and the "Fourier functions" $\exp(i\pi n)$ with $n\in\mathbb{N}$ have much in common:
- Both are eigenfunctions of the angle part of the Laplace operator.
- Both form a complete and orthonormal base of the functions on the sphere in their dimension ($S^1$ and $S^2$).
Are the spherical harmonics the $S^2$ analogon of the Fourier functions, or is there some important difference?