Wigner kernel and Gabor matrix of operators

2024/04/12 by Elena Cordero, Cordero, Elena, Gianluca Giacchi +3 · 1 citation
Mathematics · Physics and Astronomy · #Mathematical Analysis and Transform Methods #Optical and Acousto-Optic Technologies #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2404.08332

Abstract

We exhibit the connection between the Wigner kernel and the Gabor matrix of a linear bounded operator T : S(ℝ^d) → S' (ℝ^d). The smoothing effect of the Gabor matrix is highlighted by basic examples. This connection allows a comparison between the classes of Fourier integral operators defined by means of the Gabor matrix and the Wigner kernel, showing the nice off-diagonal decay of the Gabor class with respect to the Wigner kernel one and suggesting further investigations. Modulation spaces containing the Sjöstrand class are the symbol classes of this study.

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