On the characterisations of wave front sets via the short-time Fourier transform

TL;DR

This paper provides complete characterizations of initial wave front sets using the short-time Fourier transform, extending classical and Sobolev wave front concepts into a unified global framework.

Contribution

It offers new, comprehensive characterizations of wave front sets via the short-time Fourier transform, unifying local and global perspectives.

Findings

Complete characterizations of initial wave front sets via STFT

Extension of classical and Sobolev wave fronts into global versions

Unification of local and global wave front concepts

Abstract

It is well known that the classical and Sobolev wave fronts were extended into non-equivalent global versions by the use of the short-time Fourier transform. In this very short paper we give complete characterisations of initial wave front sets via the short-time Fourier transform.