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arXiv · 2407.14990

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

Vicente Asensio·Chiara Boiti·David Jornet·Alessandro Oliaro
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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.

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Vicente Asensio, Chiara Boiti, David Jornet, Alessandro Oliaro. 2024-07-20. On the compactness of the Weyl operator in $\mathcal{S}_{\omega}$. https://arxiv.org/abs/2407.14990

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