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- W3135434672 abstract "We study the link between Ψdos and Wick operators via the Bargmann transform. We deduce a formula for the symbol of the Wick operator in terms of the short-time Fourier transform of the Weyl symbol. This gives characterizations of Wick symbols of Ψdos of Shubin type and of infinite order, and results on composition. We prove a series expansion of Wick operators in terms of anti-Wick operators which leads to a sharp Gårding inequality and transition of hypoellipticity between Wick and Shubin symbols. Finally we show continuity results for anti-Wick operators, and estimates for the Wick symbols of anti-Wick operators. Nous étudions le lien entre Ψdos et opérateurs Wick passant par la transformée de Bargmann. Nous déduisons une formule pour le symbole de l'opérateur de Wick en termes de la transformée de Fourier à court terme du symbole de Weyl. Ceci donne des caractérisations des symboles Wick de Ψdos de type Shubin et d'ordre infini, et des résultats sur composition. Nous prouvons un développemet en série des opérateurs Wick dans opérateurs anti–Wick qui conduit à une forte inégalité Gårding et transition de hypoellipticité entre les symboles Wick et Shubin. Enfin, nous montrons des résultats de continuité pour opérateurs anti-Wick et des estimations pour les symboles Wick des opérateurs anti–Wick." @default.
- W3135434672 created "2021-03-15" @default.
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- W3135434672 date "2022-11-01" @default.
- W3135434672 modified "2023-09-25" @default.
- W3135434672 title "Pseudo-differential operators with isotropic symbols, Wick and anti-Wick operators, and hypoellipticity" @default.
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- W3135434672 doi "https://doi.org/10.1016/j.matpur.2022.09.002" @default.
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