Conditionally positive definite functions and Laplace-Stieltjes integrals
Journal of Approximation Theory
Radial Basis Functions
Spherical basis functions and uniform distribution of points on spheres
Journal of Approximation Theory
Stability results for approximation by positive definite functions on SO (3)
Journal of Approximation Theory
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Since radial positive definite functions on Rd remain positive definite when restricted to the sphere, it is natural to ask for properties of the zonal series expansion of such functions which relate to properties of the Fourier-Bessel transform of the radial function. We show that the decay of the Gegenbauer coefficients is determined by the behavior of the Fourier-Bessel transform at the origin.