具有分数Hausdorff维数的稀疏势
Sparse Potentials With Fractional Hausdorff Dimension
摘要：
构造了一类非随机有界离散半线Schr odinger算子，它们具有分数Hausdorff维数的纯奇异连续谱测度（在能量区间内）.为此，我们使用合适的稀疏势。我们的结果也适用于整行操作，以及某些随机操作。在后一种情况下，我们证明和计算的确切尺寸的谱措施。
英文摘要：
We construct non-random bounded discrete half-line Schr\" odinger operators which have purely singular continuous spectral measures with fractional Hausdorff dimension (in some interval of energies). To do this we use suitable sparse potentials. Our results also apply to whole line operators, as well as to certain random operators. In the latter case we prove and compute an exact dimension of the spectral measures.
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