Eigenvalues of dot-product kernels on the sphere

Abstract

We obtain explicit formulas for the eigenvalues of integral operators generated by continuous dot product kernels dened on the sphere via the usual gamma function. Using them, we present both, a procedure to describe sharp bounds for the eigenvalues and their asymptotic behavior near 0. We illustrate our results with examples, among them the integral operator gen-
erated by a Gaussian kernel .