Abstract
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.
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