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Sphere-packing in Euclidean space and extremal problems for trigonometrical polynomials. (English. Russian original) Zbl 0777.52012

Discrete Math. Appl. 1, No. 1, 69-72 (1991); translation from Diskretn. Mat. 1, No. 2, 155-158 (1989).
Summary: An upper bound for the number of disjoint spheres of radius \(\varepsilon\) in the \(n\)-dimensional torus \(T^ n\) is obtained by means of harmonic analysis. As a corollary, a new proof of Levenstein’s estimate for the density of packing of a metric space by spheres of equal radii is given.

MSC:

52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry)
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