Extremal dispositions of points on the sphere

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1997 English Publisher:Springer Science and Business Media LLCJournal:Analysis Mathematica, volume 23, pages 25-34 (issn: 0133-3852, eissn: 1588-273X,

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Authors: Kolushov, A. V.; Yudin, V. A.;

doi: 10.1007/bf02789828

Extremal dispositions of points on the sphere

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Abstract

In this paper the following problem is investigated: Dispose \(N\) points on the unit sphere \(S^{n-1}\) (in \(\mathbb R^n\)) in such a way that the sum of the distances between all pairs of points attain its maximum. Some questions are solved with properties of interpolation polynomials. Relevant to this the paper gives several interesting theorems. At the end of the paper a short information is given about the problem to dispose \(N\) points on the sphere so that the product of distances between all pairs of points is the greatest. The results were obtained in 1994.

Keywords

extremal problems, Numerical interpolation, interpolation polynomials, Inequalities and extremum problems involving convexity in convex geometry, Distance geometry, Hyperbolic and elliptic geometries (general) and generalizations, distance problems, points on the sphere, Interpolation in approximation theory, extremal dispositions of points

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