A few remarks on time-frequency analysis of Gevrey, analytic and ultra-analytic functions

TL;DR

This paper surveys recent advances in the time-frequency analysis of pseudodifferential operators, focusing on their diagonalization using Gabor frames and exploring connections with Gevrey, analytic, and ultra-analytic regularity classes.

Contribution

It introduces new links between symbol regularity classes and the time-frequency properties of associated pseudodifferential operators.

Findings

Recent results on almost diagonalization via Gabor frames

Connections between Gevrey, analytic, ultra-analytic symbols and time-frequency analysis

Enhanced understanding of pseudodifferential operators with regularity constraints

Abstract

We give a brief survey of recent results concerning almost diagonalization of pseudodifferential operators via Gabor frames. Moreover, we show new connections between symbols with Gevrey, analytic or ultra-analityc regularity and time-frequency analysis of the corresponding pseudodifferential operators.