Hermite interpolation with radial basis functions on spheres

We show how conditionally negative deenite functions on spheres coupled with strictly completely monotone functions (or functions whose derivative is strictly completely monotone) can be used for Hermite interpolation. The classes of functions thus obtained have the advantage over the strictly positive deenite functions studied in 17] that closed form representations (as opposed to series expansions) are readily available. Furthermore, our functions include the historically signiicant spherical multiquadrics. Numerical results are also presented.