Matrix analysis
Eigenvalues of differentiable positive definite kernels
SIAM Journal on Mathematical Analysis
Journal of Approximation Theory
Hyperinterpolation on the sphere at the minimal projection order
Journal of Approximation Theory
Journal of Complexity
A unified theory of radial basis functions Native Hilbert spaces for radial basis functions II
Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
Kolmogorov width of classes of smooth functions on the sphere Sd-1
Journal of Complexity
Mercer’s theorem, feature maps, and smoothing
COLT'06 Proceedings of the 19th annual conference on Learning Theory
Integral operators generated by multi-scale kernels
Journal of Complexity
Journal of Approximation Theory
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We consider integral operators on the unit sphere generated by positive definite kernels. Under smoothness conditions of Lipschitz-type on the kernel, we obtain a decay rate for the eigenvalues of the integral operator. The approach we have chosen is a multi-dimensional version, adapted to the spherical setting, of a known procedure used in the analysis of a similar problem for integral operators on the interval [0, 1]. In addition to spectral theory, the critical arguments in the paper involve the use of special covers of the sphere generated by quadrature formulas. The estimates themselves are comparable to others in the literature.