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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.14286 |
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| _version_ | 1866913214184292352 |
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| author | Demeter, Ciprian Germain, Pierre |
| author_facet | Demeter, Ciprian Germain, Pierre |
| contents | We consider spectral projectors associated to the Euclidean Laplacian on the two-dimensional torus, in the case where the spectral window is narrow. Bounds for their L2 to Lp operator norm are derived, extending the classical result of Sogge; a new question on the convolution kernel of the projector is introduced. The methods employed include l2 decoupling, small cap decoupling, and estimates of exponential sums. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_14286 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $L^2$ to $L^p$ bounds for spectral projectors on the Euclidean two-dimensional torus Demeter, Ciprian Germain, Pierre Classical Analysis and ODEs 11L07, 11P21, 42B15 We consider spectral projectors associated to the Euclidean Laplacian on the two-dimensional torus, in the case where the spectral window is narrow. Bounds for their L2 to Lp operator norm are derived, extending the classical result of Sogge; a new question on the convolution kernel of the projector is introduced. The methods employed include l2 decoupling, small cap decoupling, and estimates of exponential sums. |
| title | $L^2$ to $L^p$ bounds for spectral projectors on the Euclidean two-dimensional torus |
| topic | Classical Analysis and ODEs 11L07, 11P21, 42B15 |
| url | https://arxiv.org/abs/2306.14286 |