Wave-front sets related to quasi-analytic Gevrey sequences

TL;DR

This paper defines and investigates quasi-analytic wave-front sets associated with Gevrey sequences, analyzing their micro-local properties and how singularities propagate using Gaussian windowed Fourier transforms.

Contribution

It introduces a new class of wave-front sets for Gevrey sequences with s in [1/2,1), and studies their micro-local properties and singularity propagation.

Findings

Defined quasi-analytic wave-front sets for Gevrey sequences.

Established micro-local properties of these wave-fronts.

Analyzed propagation of singularities using Gaussian windowed transforms.

Abstract

Quasi-analytic wave-front sets of distributions which correspond to the Gevrey sequence $p!^s$, $s\in[1/2,1)$ are defined and investigated. The propagation of singularities are deduced by considering sequences of Gaussian windowed short-time Fourier transforms of distributions which are modifications of the original distributions by suitable restriction-extension techniques. Basic micro-local properties of the new wave-fronts are thereafter established.