Polynomial ultradistributions on R+d

Let G+′=G′(R+d) stand for Roumieu ultradistributions with supports in the positive cone R+d. Throughout P(G+′) denotes the algebra of continuous scalar polynomials on the space G+′. We investigate the dual pair 〈P′(G+′)∣P(G+′)〉 generated by the algebra P(G+′) and by its strong dual P′(G+′). Properties of the polynomially extended operational calculus and the semigroups of shifts along the cone R+d are considered.