On cubature with a minimal number of lines

摘要

In this paper we introduce the study of the approximation of integrals on regions of a space of dimension higher than one, by means of linear combinations of integrals on manifolds of lower dimension contained in the region of integration.This approximation arises as an alternative and/or a complement to the formulae developed first by Mysovskikh and which have knots as data.We define the notion of Gaussian formulae and we characterize the minimal representation for this approximation.