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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.14990 |
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| _version_ | 1866917729539194880 |
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| author | Asensio, Vicente Boiti, Chiara Jornet, David Oliaro, Alessandro |
| author_facet | Asensio, Vicente Boiti, Chiara Jornet, David Oliaro, Alessandro |
| contents | We characterize, using time-frequency analysis, the continuity and compactness of the Weyl operator in global classes of ultradifferentiable functions $\mathcal{S}_ω$, for weight functions $ω$ in the sense of Braun, Meise and Taylor. As a consequence, we give results about the compactness of the localization operator in $\mathcal{S}_ω$, in relation with the spaces of $ω$-multipliers and $ω$-convolutors of $\mathcal{S}_ω$. Moreover, we provide several examples that complement our investigation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14990 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the compactness of the Weyl operator in $\mathcal{S}_ω$ Asensio, Vicente Boiti, Chiara Jornet, David Oliaro, Alessandro Functional Analysis Primary 47B07, 42B35, Secondary 42C20, 46F12, We characterize, using time-frequency analysis, the continuity and compactness of the Weyl operator in global classes of ultradifferentiable functions $\mathcal{S}_ω$, for weight functions $ω$ in the sense of Braun, Meise and Taylor. As a consequence, we give results about the compactness of the localization operator in $\mathcal{S}_ω$, in relation with the spaces of $ω$-multipliers and $ω$-convolutors of $\mathcal{S}_ω$. Moreover, we provide several examples that complement our investigation. |
| title | On the compactness of the Weyl operator in $\mathcal{S}_ω$ |
| topic | Functional Analysis Primary 47B07, 42B35, Secondary 42C20, 46F12, |
| url | https://arxiv.org/abs/2407.14990 |