The cubayure formulae of L. A. Lyusternik

In this paper a short survey is given of the work of L. A. Lyusternik on cubature formulae, which are many-dimensional generalizations of the standard quadrature formulae of Gauss for an interval.
A general method is developed for constructing such formulae; a number of specific formulae are given and certain applications are made to the solution of partial differential equations.