Sur les formules de quadrature numérique dans Rⁿ avec certains noeuds ayant une composante connue

Abstract

Using the orthogonal polynomial theory, we give in this paper, conditions ensuring cubature formulae with a weight function, on compact subsets K in Rⁿwhich at some knots have a given component. The formulae are exact on the space of polynomials of n variables x_i, i=1,2,...,n,where x_i has a degree not greater than k_i + m_i,=1,2,...,n.