We characterize, using time-frequency analysis, the continuity and compactness of the Weyl operator in global classes of ultradifferentiable functions $\mathcal{S}_\omega$, for weight functions $\omega$ in the sense of Braun, Meise and Taylor. As a consequence, we give results about the compactness of the localization operator in $\mathcal{S}_\omega$, in relation with the spaces of $\omega$-multipliers and $\omega$-convolutors of $\mathcal{S}_\omega$. Moreover, we provide several examples that complement our investigation.

On the compactness of the Weyl operator in $\mathcal{S}_{\omega}$

Alessandro Oliaro.
2025-01-01

Abstract

We characterize, using time-frequency analysis, the continuity and compactness of the Weyl operator in global classes of ultradifferentiable functions $\mathcal{S}_\omega$, for weight functions $\omega$ in the sense of Braun, Meise and Taylor. As a consequence, we give results about the compactness of the localization operator in $\mathcal{S}_\omega$, in relation with the spaces of $\omega$-multipliers and $\omega$-convolutors of $\mathcal{S}_\omega$. Moreover, we provide several examples that complement our investigation.
2025
546
art. n. 129214
1
26
https://arxiv.org/abs/2407.14990
Compact Weyl operator, compact localization operator, global ultradifferentiable class, $\omega$-convolutor, $\omega$-multiplier
Vicente Asensio; Chiara Boiti; David Jornet; Alessandro Oliaro.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/2044790
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