Fourier restriction for Schatten class operators and functions on phase space
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913606891732992 |
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| author | Luef, Franz Samuelsen, Helge Jørgen |
| author_facet | Luef, Franz Samuelsen, Helge Jørgen |
| contents | We formulate a variant of Fourier restriction for operators in Schatten classes, where the Fourier-Wigner transform of a bounded operator replaces the Fourier transform of a function. The Fourier-Wigner transform is closely related to the group Fourier transform of the Heisenberg group. The first result shows that Fourier-Wigner restriction for Schatten class operators is equivalent to the restriction of the symplectic Fourier transform of functions on phase space. We deduce various Schatten class results for the quantum Fourier extension operator and answer a conjecture by Mishra and Vemuri concerning the Weyl transform of measures in the affirmative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16259 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fourier restriction for Schatten class operators and functions on phase space Luef, Franz Samuelsen, Helge Jørgen Functional Analysis Classical Analysis and ODEs 42B10, 47G30, 47B10 We formulate a variant of Fourier restriction for operators in Schatten classes, where the Fourier-Wigner transform of a bounded operator replaces the Fourier transform of a function. The Fourier-Wigner transform is closely related to the group Fourier transform of the Heisenberg group. The first result shows that Fourier-Wigner restriction for Schatten class operators is equivalent to the restriction of the symplectic Fourier transform of functions on phase space. We deduce various Schatten class results for the quantum Fourier extension operator and answer a conjecture by Mishra and Vemuri concerning the Weyl transform of measures in the affirmative. |
| title | Fourier restriction for Schatten class operators and functions on phase space |
| topic | Functional Analysis Classical Analysis and ODEs 42B10, 47G30, 47B10 |
| url | https://arxiv.org/abs/2407.16259 |