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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2508.18599 |
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| _version_ | 1866912554865917952 |
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| author | Levi, Netanel |
| author_facet | Levi, Netanel |
| contents | We study half-line discrete Schrödinger operators and their rank-one perturbations. We establish certain continuity and stability properties of the Fourier transform of the associated spectral measures. Using these results, we construct a sparse potential whose essential spectrum contains an open interval, and show that for every rank-one perturbation the corresponding spectral measure is non-Rajchman. This resolves a question posed in [24]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_18599 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a Question of Poltoratski Levi, Netanel Spectral Theory 47B36 We study half-line discrete Schrödinger operators and their rank-one perturbations. We establish certain continuity and stability properties of the Fourier transform of the associated spectral measures. Using these results, we construct a sparse potential whose essential spectrum contains an open interval, and show that for every rank-one perturbation the corresponding spectral measure is non-Rajchman. This resolves a question posed in [24]. |
| title | On a Question of Poltoratski |
| topic | Spectral Theory 47B36 |
| url | https://arxiv.org/abs/2508.18599 |