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.