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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2505.07129 |
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Table des matières:
- We construct examples of one-dimensional Schrödinger operators that illustrate the subtle nature of fractal continuity properties of spectral measures. First, we present half-line operators whose spectral measures have packing dimension zero for all boundary conditions. Second, we exhibit a whole-line operator whose spectral measure has Hausdorff dimension one, while every half-line restriction (under any boundary condition) has spectral measure of Hausdorff dimension zero. Finally, for the same whole-line operator, we prove the existence of a Borel set that carries positive spectral measure, yet has measure zero with respect to the spectral measure of the positive half-line restriction for every boundary condition.