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A0204
Title: Chebyshev-type cubature formulas on weighted spheres Authors:  Han Feng - City University of Hong Kong (Hong Kong) [presenting]
Abstract: The strict Chebyshev-type cubature formula (CF) (i.e., equal-weighted CF) is presented for doubling weights on the unit sphere equipped, with the usual surface Lebesgue measure and geodesic distance. The main interest is in the minimal number of nodes required in a strict Chebyshev-type CF. Precisely, given a normalized doubling weight on the unit sphere, we will establish the sharp asymptotic estimates of the minimal number of distinct nodes, which admits a strict Chebyshev-type CF. In addition, if the weight function is essentially bounded, the nodes involved can be configured well-separately in some sense. The proofs of these results rely on constructing new convex partitions of the unit sphere that are regular with respect to the weight. The weighted results on the unit sphere also allow us to establish similar results on strict Chebyshev-type CFs on the unit ball and the standard simplex.