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

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.


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