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On means of distances
on the surface of a sphere. II. (Upper bounds)
Gerold Wagner |
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Vol. 154 (1992), No. 2, 381–396
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Abstract |
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Given N points x1,…,xN on the unit sphere S in Euclidean d space (d ≥ 3), lower bounds for the deviation of the sum ∑ |x − xj|α, α > 1 − d; x ∈ S, from its mean value were established in terms of L1-norms in the first part of this paper. In the present part it is shown that these bounds are best possible. Our main tool is a multidimensional quadrature formula with equal weights. |
Mathematical Subject Classification 2000
Primary: 52A40
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Milestones
Received: 27 February 1991
Published: 1 June 1992
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Authors |
| Gerold Wagner | |
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