A remark on the Weyl quantisation of Paley-Wiener functions
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909502206377984 |
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| author | Samuelsen, Helge J. |
| author_facet | Samuelsen, Helge J. |
| contents | We present a short proof of the fact that the Weyl quantisation of a tempered distribution with compactly supported Fourier transform is in the Schatten $p$-class if and only if the symbol is $L^p$-integrable. The proof is based on Werner-Young's inequality from quantum harmonic analysis and a quantum version of Wiener's division lemma. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13798 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A remark on the Weyl quantisation of Paley-Wiener functions Samuelsen, Helge J. Functional Analysis Classical Analysis and ODEs 42B10, 47G30, 47B10 We present a short proof of the fact that the Weyl quantisation of a tempered distribution with compactly supported Fourier transform is in the Schatten $p$-class if and only if the symbol is $L^p$-integrable. The proof is based on Werner-Young's inequality from quantum harmonic analysis and a quantum version of Wiener's division lemma. |
| title | A remark on the Weyl quantisation of Paley-Wiener functions |
| topic | Functional Analysis Classical Analysis and ODEs 42B10, 47G30, 47B10 |
| url | https://arxiv.org/abs/2502.13798 |