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Gleichmäßige Verteilung von Punkten in gewissen metrischen Räumen, speziell auf der Kugel

Uniform distribution of points in certain metric spaces, especially on the sphere

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Abstract

To measure the uniformity of such a distribution, a new notion of discrepancy (D LV) is studied, which combines two interesting features: 1) The infinite sequences, which are uniformly distributed (in the usual sense), are characterized byD LV→0 under rather general conditions on the space. 2) Forn points on the sphere,n∈{4, 6, 12},D LV attains its minimum for the vertices of a regular polyhedron.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Salzburg, Petersbrunnstraße 19, A-5020, Salzburg, Österreich

    J. Linhart & F. Österreicher

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  1. J. Linhart
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  2. F. Österreicher
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Linhart, J., Österreicher, F. Gleichmäßige Verteilung von Punkten in gewissen metrischen Räumen, speziell auf der Kugel. Monatshefte für Mathematik 89, 111–120 (1980). https://doi.org/10.1007/BF01476589

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