Poisson summation formula in weighted Lebesgue spaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910737785421824 |
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| author | Saucedo, Miquel Tikhonov, Sergey |
| author_facet | Saucedo, Miquel Tikhonov, Sergey |
| contents | We characterize the parameters $(α,β,p,q)$ for which the condition $f|x|^α\in L^p$ and $\widehat{f}|ξ|^β\in L^q$ implies the validity of the Poisson summation formula, thus completing the study of Kahane and Lemarié-Rieusset. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07661 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Poisson summation formula in weighted Lebesgue spaces Saucedo, Miquel Tikhonov, Sergey Classical Analysis and ODEs 42B10, 42B35 (Primary) 46E30 (Secondary) We characterize the parameters $(α,β,p,q)$ for which the condition $f|x|^α\in L^p$ and $\widehat{f}|ξ|^β\in L^q$ implies the validity of the Poisson summation formula, thus completing the study of Kahane and Lemarié-Rieusset. |
| title | Poisson summation formula in weighted Lebesgue spaces |
| topic | Classical Analysis and ODEs 42B10, 42B35 (Primary) 46E30 (Secondary) |
| url | https://arxiv.org/abs/2412.07661 |