One-Step Recurrences for Stationary Random Fields on the Sphere - Beatson, R.K.; W. zu Castell (Symmetry, Integrability and Geometry: Methods and Applications, 2016)
This paper develops operators for zonal functions on the sphere which preserve (strict) positive definiteness while moving up and down in the ladder of dimensions by steps of one. These fractional operators are constructed to act appropriately on the Gegenbauer polynomials Cλn.