Wigner kernel and Gabor matrix of operators
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929312263831552 |
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| author | Cordero, Elena Giacchi, Gianluca Rodino, Luigi |
| author_facet | Cordero, Elena Giacchi, Gianluca Rodino, Luigi |
| contents | 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 Sjöstrand class are the symbol classes of this study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08332 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wigner kernel and Gabor matrix of operators Cordero, Elena Giacchi, Gianluca Rodino, Luigi Analysis of PDEs 35S05, 35S30, 42C15 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 Sjöstrand class are the symbol classes of this study. |
| title | Wigner kernel and Gabor matrix of operators |
| topic | Analysis of PDEs 35S05, 35S30, 42C15 |
| url | https://arxiv.org/abs/2404.08332 |