On the continuous dual of a polynomial bialgebra

This paper is devoted to the study of the dual bialgebra [image omitted]  of the bialgebra Bn of polynomials in finitely many variables. The elements of [image omitted]  are described in various ways in orcer to obtain some useful formulae (e.g., a formula for the "remainder" modulo a cofinite ideal of Bn). The subcoalgebra Cf generated by a given element of [image omitted]  is studied and its structure constants with respect to different natural bases are given.