The paper "On the constant in a transference inequality for the vector-valued Fourier transform" revisited
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866918299410890752 |
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| author | van Neerven, Dion Gijswijt. Jan |
| author_facet | van Neerven, Dion Gijswijt. Jan |
| contents | The standard proof of the equivalence of Fourier type on \(\mathbb R^d\) and on the torus \(\mathbb T^d\) is usually stated in terms of an implicit constant which can be expressed in terms of the global minimiser of the functions \[f_r(x)=\sum_{m\in\mathbb{Z}}\left|\frac{\sin(π(x+m))}{π(x+m)}\right|^{2r},\qquad x\in [0,1], \ r\ge 1.\] The aim of this note is to provide a short proof of a result of the authors which states that each \(f_r\) takes a global minimum at the point \(x = \frac12\). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15454 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The paper "On the constant in a transference inequality for the vector-valued Fourier transform" revisited van Neerven, Dion Gijswijt. Jan Classical Analysis and ODEs The standard proof of the equivalence of Fourier type on \(\mathbb R^d\) and on the torus \(\mathbb T^d\) is usually stated in terms of an implicit constant which can be expressed in terms of the global minimiser of the functions \[f_r(x)=\sum_{m\in\mathbb{Z}}\left|\frac{\sin(π(x+m))}{π(x+m)}\right|^{2r},\qquad x\in [0,1], \ r\ge 1.\] The aim of this note is to provide a short proof of a result of the authors which states that each \(f_r\) takes a global minimum at the point \(x = \frac12\). |
| title | The paper "On the constant in a transference inequality for the vector-valued Fourier transform" revisited |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2601.15454 |