arXiv
Open Access
2025
On a Question of Poltoratski
Netanel Levi
Abstrak
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].
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Netanel Levi
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- 2025
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