Micro-local analysis in some spaces of ultradistributions

TL;DR

This paper extends wave-front set analysis to broader ultradistribution spaces, relating them to classical wave-front sets and using Gabor frames to connect discrete and continuous wave-front sets.

Contribution

It introduces new results on wave-front sets in ultradistribution spaces and demonstrates their equivalence with classical wave-front sets using Gabor frame techniques.

Findings

Wave-front sets in ultradistribution spaces are characterized.

Discrete and continuous wave-front sets are shown to coincide.

Extensions of previous results to broader ultradistribution classes.

Abstract

In this paper we extend some results from our earlier papers on wave-front sets, concerning wave-front sets of Fourier-Lebesgue and modulation space types, to a broader class of spaces of ultradistributions, and relate these wave-front sets with the usual wave-front sets of ultradistributions. Furthermore, we use Gabor frames for the description of discrete wave-front sets, and prove that these wave-front sets coincide with corresponding continuous ones.