Sharp embeddings between weighted Paley-Wiener spaces
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arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912850063130624 |
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| author | Carneiro, Emanuel González-Riquelme, Cristian Oliveira, Lucas Olivo, Andrea Ombrosi, Sheldy Ramos, Antonio Pedro Sousa, Mateus |
| author_facet | Carneiro, Emanuel González-Riquelme, Cristian Oliveira, Lucas Olivo, Andrea Ombrosi, Sheldy Ramos, Antonio Pedro Sousa, Mateus |
| contents | In this paper we address the problem of estimating the operator norm of the embeddings between multidimensional weighted Paley-Wiener spaces. These can be equivalently thought as Fourier uncertainty principles for bandlimited functions. By means of radial symmetrization mechanisms, we show that such problems can all be shifted to dimension one. We provide precise asymptotics in the general case and, in some particular situations, we are able to identify the sharp constants and characterize the extremizers. The sharp constant study is actually a consequence of a more general result we prove in the setup of de Branges spaces of entire functions, addressing the operator given by multiplication by $z^k$, $k \in \mathbb{N}$. Applications to sharp higher order Poincaré inequalities and other related extremal problems are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_06442 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sharp embeddings between weighted Paley-Wiener spaces Carneiro, Emanuel González-Riquelme, Cristian Oliveira, Lucas Olivo, Andrea Ombrosi, Sheldy Ramos, Antonio Pedro Sousa, Mateus Classical Analysis and ODEs Analysis of PDEs 46E22, 42A05, 42B35, 30H45, 33C10 In this paper we address the problem of estimating the operator norm of the embeddings between multidimensional weighted Paley-Wiener spaces. These can be equivalently thought as Fourier uncertainty principles for bandlimited functions. By means of radial symmetrization mechanisms, we show that such problems can all be shifted to dimension one. We provide precise asymptotics in the general case and, in some particular situations, we are able to identify the sharp constants and characterize the extremizers. The sharp constant study is actually a consequence of a more general result we prove in the setup of de Branges spaces of entire functions, addressing the operator given by multiplication by $z^k$, $k \in \mathbb{N}$. Applications to sharp higher order Poincaré inequalities and other related extremal problems are discussed. |
| title | Sharp embeddings between weighted Paley-Wiener spaces |
| topic | Classical Analysis and ODEs Analysis of PDEs 46E22, 42A05, 42B35, 30H45, 33C10 |
| url | https://arxiv.org/abs/2304.06442 |