A sequential approach to ultradistribution spaces

Abstract

We introduce and investigate two types of the space U * of s-ultradistributions meant as equivalence classes of suitably defined fundamental sequences of smooth functions; we prove the existence of an isomorphism between U * and the respective space D ′ * of ultradistributions: of Beurling type if * = (p! t) and of Roumieu type if * = {p! t }. We also study the spaces T * and T * of t-ultradistributions andt-ultradistributions, respectively, and show that these spaces are isomorphic with the space S ′ * of tempered ultradistributions both in the Beurling and the Roumieu case.