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arXiv · 2404.08332

Wigner kernel and Gabor matrix of operators

Elena Cordero·Gianluca Giacchi·Luigi Rodino
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Abstract

We exhibit the connection between the Wigner kernel and the Gabor matrix of a linear bounded operator T : $\mathcal{S}(\mathbb{R}^d) \to \mathcal{S}' (\mathbb{R}^d)$. 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 Sj\"ostrand class are the symbol classes of this study.

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Elena Cordero, Gianluca Giacchi, Luigi Rodino. 2024-04-12. Wigner kernel and Gabor matrix of operators. https://arxiv.org/abs/2404.08332

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