×

Problems of approximation theory in discrete geometry. (English) Zbl 1081.52504

Haußmann, Werner (ed.) et al., Advances in multivariate approximation. Proceedings of the 3rd international conference on multivariate approximation theory, Witten-Bommerholz, Germany, September 27–October 2, 1998. Berlin: Wiley-VCH (ISBN 3-527-40236-5/hbk). Math. Res. 107, 19-32 (1999).
From the text: There is a list of old interesting problems in \(\mathbb{R}^3\) on the best arrangement of points on a sphere. Such problems arise in different fields of science. The multidimensional analogues of these problems are of prominent interest in coding theory. Essential progress in this field has been achieved during the last 20–30 years. To solve such a problem, one should make two steps: First find an extremal point distribution, then prove that it is the best possible. In the second step, i.e., in finding estimates for optimal parameters of the arrangement, analytical methods which use extremal properties of polynomials and functions are used. This paper is devoted to problems where optimal parameters are obtained using Fourier analysis.
In section 4 extremal problems on a torus are studied.
For the entire collection see [Zbl 0931.00036].

MSC:

52C35 Arrangements of points, flats, hyperplanes (aspects of discrete geometry)
52C15 Packing and covering in \(2\) dimensions (aspects of discrete geometry)
41A30 Approximation by other special function classes
52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry)
52C26 Circle packings and discrete conformal geometry

Keywords:

sphere; torus
PDFBibTeX XMLCite