Energies, group-invariant kernels and numerical integration on compact manifolds

Authors:
S. B. Damelin;J. Levesley;D. L. Ragozin;X. Sun
Affiliations:
Department of Mathematical Sciences, Georgia Southern University, Postoffice Box 8093, Statesboro, GA 30460-8093, USA;Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK;Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195-4350, USA;Department of Mathematics, 10M Cheek Hall, Missouri State University Springfield, MO 65897, USA
Venue:
Journal of Complexity
Year:
2009

Citing 4
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Abstract

The purpose of this paper is to derive quadrature estimates on compact, homogeneous manifolds embedded in Euclidean spaces, via energy functionals associated with a class of group-invariant kernels which are generalizations of zonal kernels on the spheres or radial kernels in euclidean spaces. Our results apply, in particular, to weighted Riesz kernels defined on spheres and certain projective spaces. Our energy functionals describe both uniform and perturbed uniform distribution of quadrature point sets.