Completeness of uniformly discrete translates in $L^p(\mathbb{R})$
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916557343424512 |
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| author | Lev, Nir |
| author_facet | Lev, Nir |
| contents | We construct a real sequence $\{λ_n\}_{n=1}^{\infty}$ satisfying $λ_n = n + o(1)$, and a Schwartz function $f$ on $\mathbb{R}$, such that for any $N$ the system of translates $\{f(x - λ_n)\}$, $n > N$, is complete in the space $L^p(\mathbb{R})$ for every $p>1$. The same system is also complete in a wider class of Banach function spaces on $\mathbb{R}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15588 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Completeness of uniformly discrete translates in $L^p(\mathbb{R})$ Lev, Nir Classical Analysis and ODEs Functional Analysis 42A65, 46E30, 46E50 We construct a real sequence $\{λ_n\}_{n=1}^{\infty}$ satisfying $λ_n = n + o(1)$, and a Schwartz function $f$ on $\mathbb{R}$, such that for any $N$ the system of translates $\{f(x - λ_n)\}$, $n > N$, is complete in the space $L^p(\mathbb{R})$ for every $p>1$. The same system is also complete in a wider class of Banach function spaces on $\mathbb{R}$. |
| title | Completeness of uniformly discrete translates in $L^p(\mathbb{R})$ |
| topic | Classical Analysis and ODEs Functional Analysis 42A65, 46E30, 46E50 |
| url | https://arxiv.org/abs/2401.15588 |