Metaplectic Wigner distributions

Gianluca Giacchi

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arXiv · 2212.06818

Metaplectic Wigner distributions

Gianluca Giacchi

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Abstract

Metaplectic Wigner distributions were recently investigated as natural generalizations of the classical Wigner distribution, and provide a wide class of time-frequency representations that exploits the structure of the symplectic group. This work serves as a survey on metaplectic Wigner distributions and their applications to the time-frequency analysis of modulation spaces and pseudodifferential operators, topics that are all still poorly understood. We also give some new results, generalizing Lieb's uncertainty principle to the so-called matrix Wigner distributions and proving the continuity on $M^p_{v_s}(\mathbb{R}^d)$ spaces of metaplectic pseudodifferential operators with symbols in $M^{p'}_{v_{-s}}(\mathbb{R}^d)$.

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Gianluca Giacchi. 2022-12-13. Metaplectic Wigner distributions. https://arxiv.org/abs/2212.06818

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