A Few Remarks on Time-frequency Analysis of Gevrey, Analytic and Ultra-analytic Functions
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.
KeywordsPseudodifferential operators Gelfand–Shilov spaces Gevrey spaces short-time Fourier transform Gabor frames
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