Sampling projections in the uniform norm
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916980734296064 |
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| author | Krieg, David Pozharska, Kateryna Ullrich, Mario Ullrich, Tino |
| author_facet | Krieg, David Pozharska, Kateryna Ullrich, Mario Ullrich, Tino |
| contents | We show that there are sampling projections on arbitrary $n$-dimensional subspaces of $B(D)$ with at most $2n$ samples and norm of order $\sqrt{n}$, where $B(D)$ is the space of complex-valued bounded functions on a set $D$. This gives a more explicit form of the Kadets-Snobar theorem for the uniform norm and improves upon Auerbach's lemma. We discuss consequences for optimal recovery in $L_p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02220 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sampling projections in the uniform norm Krieg, David Pozharska, Kateryna Ullrich, Mario Ullrich, Tino Functional Analysis Numerical Analysis 41A65 (Primary) 41A50, 46B09 (Secondary) We show that there are sampling projections on arbitrary $n$-dimensional subspaces of $B(D)$ with at most $2n$ samples and norm of order $\sqrt{n}$, where $B(D)$ is the space of complex-valued bounded functions on a set $D$. This gives a more explicit form of the Kadets-Snobar theorem for the uniform norm and improves upon Auerbach's lemma. We discuss consequences for optimal recovery in $L_p$. |
| title | Sampling projections in the uniform norm |
| topic | Functional Analysis Numerical Analysis 41A65 (Primary) 41A50, 46B09 (Secondary) |
| url | https://arxiv.org/abs/2401.02220 |