  The paper introduces a new characterisation of strictly positive definiteness
for kernels on the 2-sphere without assuming the kernel to be radially
(isotropic) or axially symmetric. The results use the series expansion of the
kernel in spherical harmonics. Then additional sufficient conditions are proven
for kernels with a block structure of expansion coefficients. These generalise
the result derived by Chen et al. 2003 for radial kernels to non-radial
kernels.
