Schauder frames of discrete translates in $L^2(\mathbb{R})$
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912777604431872 |
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| author | Lev, Nir Tselishchev, Anton |
| author_facet | Lev, Nir Tselishchev, Anton |
| contents | We construct a uniformly discrete sequence $\{λ_1 < λ_2 < \cdots\} \subset \mathbb{R}$ and functions $g$ and $\{g_n^*\}$ in $L^2(\mathbb{R})$, such that every $f \in L^2(\mathbb{R})$ admits a series expansion \[ f(x) = \sum_{n=1}^{\infty} \langle f, g_n^* \rangle \, g(x-λ_n) \] convergent in the $L^2(\mathbb{R})$ norm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11039 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Schauder frames of discrete translates in $L^2(\mathbb{R})$ Lev, Nir Tselishchev, Anton Classical Analysis and ODEs Functional Analysis 42A10, 42C15, 46B15 We construct a uniformly discrete sequence $\{λ_1 < λ_2 < \cdots\} \subset \mathbb{R}$ and functions $g$ and $\{g_n^*\}$ in $L^2(\mathbb{R})$, such that every $f \in L^2(\mathbb{R})$ admits a series expansion \[ f(x) = \sum_{n=1}^{\infty} \langle f, g_n^* \rangle \, g(x-λ_n) \] convergent in the $L^2(\mathbb{R})$ norm. |
| title | Schauder frames of discrete translates in $L^2(\mathbb{R})$ |
| topic | Classical Analysis and ODEs Functional Analysis 42A10, 42C15, 46B15 |
| url | https://arxiv.org/abs/2312.11039 |