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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.18599 |
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Table of 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].