Hereditary completeness for systems of exponentials in weighted $L^2$-spaces
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915599392702464 |
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| author | Semenov, Andrei V. |
| author_facet | Semenov, Andrei V. |
| contents | We prove that for a weight $w$, which has at least polynomial decay, there exists a complete and minimal system $\{e^{iλ_n t}\}_{n\in \mathbb{N}}$ of exponentials in weighted space $L^2(w)$ on $(-π,π)$, which is not hereditarily complete. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18131 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hereditary completeness for systems of exponentials in weighted $L^2$-spaces Semenov, Andrei V. Complex Variables Functional Analysis 30A10, 30H20 We prove that for a weight $w$, which has at least polynomial decay, there exists a complete and minimal system $\{e^{iλ_n t}\}_{n\in \mathbb{N}}$ of exponentials in weighted space $L^2(w)$ on $(-π,π)$, which is not hereditarily complete. |
| title | Hereditary completeness for systems of exponentials in weighted $L^2$-spaces |
| topic | Complex Variables Functional Analysis 30A10, 30H20 |
| url | https://arxiv.org/abs/2503.18131 |