Minimal Weighted $4$-Designs on the Sphere~$S^2$
Matematičeskie zametki, Tome 91 (2012) no. 5, pp. 787-790.

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Keywords: minimal weighted $t$-design
Mots-clés : cubature formula, algebraic polynomial, Gegenbauer polynomial, Jacobi polynomial, Legendre polynomial.
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A. V. Bondarenko; D. V. Gorbachev. Minimal Weighted $4$-Designs on the Sphere~$S^2$. Matematičeskie zametki, Tome 91 (2012) no. 5, pp. 787-790. http://geodesic.mathdoc.fr/item/MZM_2012_91_5_a15/

[1] D. V. Gorbachev, Izv. TulGU. Ser. Matem. Mekh. Inform., 5:3 (1999), 33–37 | MR

[2] D. V. Gorbachev, Izv. TulGU. Ser. Estestv. nauki, 2010, no. 2, 15–23

[3] A. Bondarenko, D. Radchenko, M. Viazovska, Optimal Asymptotic Bounds for Spherical Designs, 2011, arXiv: math.MG/1009.4407v3

[4] I. P. Mysovskikh, Interpolyatsionnye kubaturnye formuly, Nauka, M., 1981 | MR | Zbl

[5] N. N. Andreev, Matem. zametki, 67:4 (2000), 489–497 | MR | Zbl

[6] P. Delsarte, J. M. Goethals, J. J. Seidel, Geom. Dedicata, 6:3 (1977), 363–388 | DOI | MR | Zbl

[7] V. A. Yudin, Izv. RAN. Ser. matem., 61:3 (1997), 213–223 | MR | Zbl

[8] S. Heo, Y. Xu, J. Comput. Appl. Math., 112:1-2 (1999), 95–119 | MR | Zbl