Sampling on Paley-Wiener spaces on graphs, with particular focus on the infinite-dimensional case
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911727862415360 |
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| author | Giannoni, Filippo |
| author_facet | Giannoni, Filippo |
| contents | We prove a sampling theorem for infinite-dimensional Paley-Wiener spaces on graphs which allows for stable frame reconstruction. We prove that all sampling sets for a fixed Paley-Wiener space are complements of lambda-sets (i.e. sets where a Poincaré-type inequality holds), thereby providing a sufficient condition for stable sampling and reconstruction on graphs such as $\mathbb{Z}^n$-lattices and radial trees with finite geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17343 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sampling on Paley-Wiener spaces on graphs, with particular focus on the infinite-dimensional case Giannoni, Filippo Functional Analysis 43A85, 05C99, 94A20 (Primary) 94A12 (Secondary) We prove a sampling theorem for infinite-dimensional Paley-Wiener spaces on graphs which allows for stable frame reconstruction. We prove that all sampling sets for a fixed Paley-Wiener space are complements of lambda-sets (i.e. sets where a Poincaré-type inequality holds), thereby providing a sufficient condition for stable sampling and reconstruction on graphs such as $\mathbb{Z}^n$-lattices and radial trees with finite geometry. |
| title | Sampling on Paley-Wiener spaces on graphs, with particular focus on the infinite-dimensional case |
| topic | Functional Analysis 43A85, 05C99, 94A20 (Primary) 94A12 (Secondary) |
| url | https://arxiv.org/abs/2511.17343 |