Fourier-Wigner multipliers and the Bochner-Riesz conjecture for Schatten class operators
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913724328050688 |
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| author | Samuelsen, Helge Jørgen |
| author_facet | Samuelsen, Helge Jørgen |
| contents | In this paper we introduce the notion of Fourier-Wigner multipliers for the Schatten class operators $\mathcal{S}^p$, which acts as an extension of classical localisation operators in time-frequency analysis. We establish results about Fourier-Wigner multipliers through convolution with rank-one operators and Werner-Young's inequality. We are also able to prove an equivalence relation for compactly supported Fourier multipliers. This allows us to reformulate the Bochner-Riesz conjecture in terms of Schatten class operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16248 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fourier-Wigner multipliers and the Bochner-Riesz conjecture for Schatten class operators Samuelsen, Helge Jørgen Functional Analysis Classical Analysis and ODEs 42B10, 42B15, 47G30, 47B10 In this paper we introduce the notion of Fourier-Wigner multipliers for the Schatten class operators $\mathcal{S}^p$, which acts as an extension of classical localisation operators in time-frequency analysis. We establish results about Fourier-Wigner multipliers through convolution with rank-one operators and Werner-Young's inequality. We are also able to prove an equivalence relation for compactly supported Fourier multipliers. This allows us to reformulate the Bochner-Riesz conjecture in terms of Schatten class operators. |
| title | Fourier-Wigner multipliers and the Bochner-Riesz conjecture for Schatten class operators |
| topic | Functional Analysis Classical Analysis and ODEs 42B10, 42B15, 47G30, 47B10 |
| url | https://arxiv.org/abs/2502.16248 |