Expansion of a real function on 2-sphere in spherical harmonics, so-called Laplace series, converges uniformly for continuously differentiable functions (see e.g. https://projecteuclid.org/euclid.bbms/1103408694).
Is there any explicit example of a real function on 2-sphere, which is merely continuous, and for which the corresponding Laplace series does not converge uniformly? I would expect that this is some "fractal beast", but I might be wrong...