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 and ?t-ultradistributions, respectively, and show that these spaces are isomorphic with the space S?* of tempered ultradistributions both in the Beurling and the Roumieu case.