On a Question of Poltoratski

Netanel Levi

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arXiv · 2508.18599

On a Question of Poltoratski

Netanel Levi

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Abstract

We study half-line discrete Schr\"odinger 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. 2025-08-26. On a Question of Poltoratski. https://arxiv.org/abs/2508.18599

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