Yudin, V. A. Extremality properties of functions and designs on the torus. (English. Russian original) Zbl 0923.41021 Math. Notes 61, No. 4, 530-533 (1997); translation from Mat. Zametki 61, No. 4, 637-640 (1997). A design is a set of points for which a certain cubature formula holds for integrals over the \(n\)-torus. The author gives lower estimates for the minimal number of points building up a design. Reviewer: J.Appell (Würzburg) Cited in 1 Document MSC: 41A99 Approximations and expansions 42A65 Completeness of sets of functions in one variable harmonic analysis PDFBibTeX XMLCite \textit{V. A. Yudin}, Math. Notes 61, No. 4, 530--533 (1997; Zbl 0923.41021); translation from Mat. Zametki 61, No. 4, 637--640 (1997) Full Text: DOI References: [1] I. P. Mysovskikh,Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],296, No. 1, 28–31 (1987). [2] M. Beckers and M. Cools,Inter. Series of Numer. Math.,112, 13–24 (1993). · Zbl 0797.41026 [3] A. V. Reztsov,Mat. Zametki [Math. Notes],48, No. 1, 151–152 (1990). [4] B. Reznick,Mem. Amer. Math. Soc.,96, No. 463 (1992). [5] J. Seidel,Diskrete Math.,136, 281–293 (1994). · Zbl 0813.05015 [6] V. A. Yudin,Discretnaya Matematika,1, No. 2, 155–158 (1989). [7] E. M. Stein and G. Weiss,Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, N.J. (1974). · Zbl 0294.42003 [8] G. N. Watson,A Treatise on the Theory of Bessel Functions, Cambridge Univ. Press, Cambridge (1945). · Zbl 0063.08185 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.