Characterization of Wave Fronts of Ultradistributions Using Directional Short-Time Fourier Transform

In this paper we give a characterization of Sobolev k-directional wave front of order p∈[1,∞) of tempered ultradistributions via the directional short-time Fourier transform.

Wilson Bases and Ultradistributions

We provide a characterization of the Gelfand–Shilov-type spaces of test functions and their dual spaces of tempered ultradistributions by means of Wilson bases of exponential decay. We offer two different proofs and extend known results to the Roumieu case.

Characterization of the w-Tempered ultradistributions

We use apreviously obtained characterization of test functions of w-Tempered Ultradistributions to charcterize the space w-Tempered Ultradistributions using Riesz representation Theorem.

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!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.