Decoupling for Schatten class operators in the setting of Quantum Harmonic Analysis
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913606912704512 |
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| author | Samuelsen, Helge Jørgen |
| author_facet | Samuelsen, Helge Jørgen |
| contents | We introduce the notion of decoupling for operators, and prove an equivalence between classical $\ell^qL^p$ decoupling for functions and $\ell^q\mathcal{S}^p$ decoupling for operators on bounded sets in $\mathbb{R}^{2d}$. We also show that the equivalence only depends on the bounded set $Ω$, and not the values of $p,q$ nor the partition of $Ω$. The proof relies on a quantum version of Wiener's division lemma. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17109 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Decoupling for Schatten class operators in the setting of Quantum Harmonic Analysis Samuelsen, Helge Jørgen Functional Analysis Classical Analysis and ODEs 42B10, 42B15, 47G30, 47B10 We introduce the notion of decoupling for operators, and prove an equivalence between classical $\ell^qL^p$ decoupling for functions and $\ell^q\mathcal{S}^p$ decoupling for operators on bounded sets in $\mathbb{R}^{2d}$. We also show that the equivalence only depends on the bounded set $Ω$, and not the values of $p,q$ nor the partition of $Ω$. The proof relies on a quantum version of Wiener's division lemma. |
| title | Decoupling for Schatten class operators in the setting of Quantum Harmonic Analysis |
| topic | Functional Analysis Classical Analysis and ODEs 42B10, 42B15, 47G30, 47B10 |
| url | https://arxiv.org/abs/2407.17109 |