A sequential approach to ultradistribution spaces

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!) and of Roumieu type if ∗ = {p!}. We also study the spaces T ∗ and T̃ ∗ of t-ultradistributions and t̃-ultradistributions, respectively, and show that these spaces are isomorphic with the space S of tempered ultradistributions both in the Beurling and the Roumieu case.