A Logvinenko-Sereda theorem for lacunary spectra
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914414468268032 |
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| author | Saucedo, Miquel Tikhonov, Sergey |
| author_facet | Saucedo, Miquel Tikhonov, Sergey |
| contents | For a function $F$ represented as $F(x)=\sum_{n=0}^\infty{f_n (x) e^{2 πi λ_n x}},$ where each $f_n$ satisfies $\operatorname{spec}(f_n) \subset [0, 1]$ and $(λ_n)_{n\geq 0}\subset \mathbb{R}_+$ is a lacunary sequence, we obtain $$ \|F\|_{L^2(\mathbb{R})}\lesssim \|Fχ_{E}\|_{L^2(\mathbb{R})} $$ provided that $E$ is a thick subset of $\mathbb{R}$. This extends the Logvinenko-Sereda theorem and answers a question posed by Kovrizhkin for functions with positive frequencies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21950 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Logvinenko-Sereda theorem for lacunary spectra Saucedo, Miquel Tikhonov, Sergey Classical Analysis and ODEs 2B10, 42A55 For a function $F$ represented as $F(x)=\sum_{n=0}^\infty{f_n (x) e^{2 πi λ_n x}},$ where each $f_n$ satisfies $\operatorname{spec}(f_n) \subset [0, 1]$ and $(λ_n)_{n\geq 0}\subset \mathbb{R}_+$ is a lacunary sequence, we obtain $$ \|F\|_{L^2(\mathbb{R})}\lesssim \|Fχ_{E}\|_{L^2(\mathbb{R})} $$ provided that $E$ is a thick subset of $\mathbb{R}$. This extends the Logvinenko-Sereda theorem and answers a question posed by Kovrizhkin for functions with positive frequencies. |
| title | A Logvinenko-Sereda theorem for lacunary spectra |
| topic | Classical Analysis and ODEs 2B10, 42A55 |
| url | https://arxiv.org/abs/2603.21950 |