Wave front sets with respect to Banach spaces of ultradistributions. Characterisation via the short-time Fourier transform

TL;DR

This paper introduces ultradistributional wave front sets relative to specific Banach spaces of ultradistributions and characterizes them using the short-time Fourier transform, advancing the understanding of ultradistribution analysis.

Contribution

It defines ultradistributional wave front sets with respect to translation-modulation invariant Banach spaces and provides their characterization via the short-time Fourier transform.

Findings

Wave front sets are characterized by the short-time Fourier transform.

Ultradistributional wave front sets are defined with respect to specific Banach spaces.

The approach generalizes classical wave front set analysis.

Abstract

We define ultradistributional wave front sets with respect to translation-modulation invariant Banach spaces of ultradistributions having solid Fourier image. The main result is their characterisation by the short-time Fourier transform.