From Fourier to Gegenbauer: Dimension walks on spheres

Abstract

We show that the even- resp. odd-dimensional Schoenberg coefficients in Gegenbauer expansions of isotropic positive definite functions on the d-sphere can be expressed as linear combinations of Fourier resp. Legendre coefficients, and we give closed form expressions for the coefficients involved in these expansions.

References in corpus (2)

• Isotropic Gaussian random fields on the sphere: Regularity, fast simulation and stochastic partial differential equations
• Convolution roots and differentiability of isotropic positive definite functions on spheres