Aspects of Gaussian Processes on Spheres.

We review the Dudley integral for the Belyaev dichotomy applied to Gaussian processes on spheres, and discuss the approximate (or restricted) continuity of paths in the discontinuous case. In the continuous case, we investigate the link between the smoothness of paths and the decay rate of the angular power spectrum, following Tauberian work of the first author, Malyarenko, and Lang and Schwab. We develop the work of the first author on projection from spheres of higher to those of lower dimension, transforming the numerically intractable series for the relevant density into a numerically tractable double integral.