A generalization of Muirheadʹs theorem Original Research Article

For a finite group G of linear transformations of a real vector space V it is proved that the set of points where for every linear function ξ on V the function z maps to ∑gset membership, variantGexp [ξ(gz)] does not exceed its value at x set membership, variant V coincides with the convex hull of the G-orbit of x. A few inequalities are derived from this result.