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Hirao, Masatake; Okuda, Takayuki; Sawa, Masanori

Some remarks on cubature formulas with linear operators. (English) Zbl 1347.41038

J. Math. Soc. Japan 68, No. 2, 711-735 (2016).
In this paper, the authors define operator-type cubature formulas as a generalization of Laplacian-type cubature formulas and classical polynomial-type cubature formulas, and study a Stroud-type inequality for operator-type cubature. Moreover, a generalization of well-known Sobolev’s theorem on invariant polynomial-type cubature to operator-type cubature is given.
Reviewer: Yuri A. Farkov (Moscow)

MSC:

41A55 Approximate quadratures
65D32 Numerical quadrature and cubature formulas
05E99 Algebraic combinatorics
15A63 Quadratic and bilinear forms, inner products

Keywords:

cubature formula; Stroud-type inequality; Fisher-type inequality; operator-type cubature; Sobolev’s theorem; Sylvester’s law of inertia
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\textit{M. Hirao} et al., J. Math. Soc. Japan 68, No. 2, 711--735 (2016; Zbl 1347.41038)
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