On minimal cubature formulas exact for Haar polynomials of low degrees in the two-dimensional case
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 3, pp. 318-323.

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A lower estimate for number of nodes of cubature formulas possessing the Haar $d$-property ($d \geqslant 2$) is obtained in the two-dimensional case. Examples of minimal cubature formulas with Haar $d$-property for $d=2$ and $d=3$ are given.
Keywords: minimal cubature formulas, Haar functions, Haar polynomials, Haar $d$-property.
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Kirill A. Kirillov. On minimal cubature formulas exact for Haar polynomials of low degrees in the two-dimensional case. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 3, pp. 318-323. http://geodesic.mathdoc.fr/item/JSFU_2014_7_3_a5/

[1] I. M. Sobol’, Multidimensional Quadrature Formulas and Haar Functions, Nauka, M., 1969 (in Russian) | MR

[2] K. A. Kirillov, M. V. Noskov, “Minimal quadrature formulas accurate for Haar polynomials”, Comput. Math. Phys., 42:6 (2002), 758–766 | MR | Zbl

[3] K. A. Kirillov, “Lower estimates for node number of cubature formulas exact for Haar polynomials in two-dimensional case”, Vychislitelnye tekhnologii, 9, special issue (2004), 62–71 (in Russian) | Zbl

[4] K. A. Kirillov, “Construction of minimal cubature formulas exact for Haar polynomials of high degrees in two-dimensional case”, Vychislitelnye tekhnologii, 10, special issue (2005), 29–47 (in Russian) | Zbl

[5] A. Haar, “Zur Theorie der Orthogonalen Funktionensysteme”, Math. Ann., 69 (1910), 331–371 | DOI | MR | Zbl

[6] I. P. Mysovskikh, Interpolation Cubature Formulas, Nauka, M., 1981 (in Russian) | MR | Zbl

[7] I. P. Mysovskikh, “Cubature formulas exact for trigonometric polynomials”, Metody Vychislenii, Leningrad, Leningradsky Gosudarstvenny Universitet, 15 (1988), 7–19 (in Russian) | MR | Zbl