ORTHOGONAL POLYNOMIALS AND SOME CUBATURE FORMULAS FOR AN INTEGRAL WITH RADIALLY SYMMETRICAL WEIGHT

For the linear space of polynomials of degree t, orthogonal with respect to an n-dimensional integral with a radially symmetric weight, a decomposition into a direct sum of subspaces is established, governed by the Gauss representation of the form of the leading terms. Cubature formulae are constructed, whose structure is connected with this decomposition.