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

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.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1209.094