Cubature formulae which are exact on spacesP, intermediate betweenPk andQk′

SummaryIn this paper we search, from the orthogonal polynomial theory, for conditions which allow to obtain cubature formulae on compacts of ℝn, with weight function, and which are exact on the spaceR(k1, k2, ..., kn) of all polynomials of degree ≦ki respectively to each variablexi, 1≦i≦n.