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arXiv · 1912.09688

An Upbound of Hausdorff's Dimension of the Divergence Set of the fractional Schr\"odinger Operator on $H^s(\mathbb R^n)

Dan Li·Junfeng Li·Jie Xiao
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Abstract

This paper shows $$ \sup_{f\in H^s(\mathbb{R}^n)}\dim _H\left\{x\in\mathbb{R}^n:\ \lim_{t\rightarrow0}e^{it(-\Delta)^\alpha}f(x)\neq f(x)\right\}\leq n+1-\frac{2(n+1)s}{n}\ \ \text{under}\ \ \begin{cases} n\geq2;\\ \alpha>\frac12; \frac{n}{2(n+1)}<s\leq\frac{n}{2} . \end{cases} $$

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Dan Li, Junfeng Li, Jie Xiao. 2019-12-20. An Upbound of Hausdorff's Dimension of the Divergence Set of the fractional Schr\"odinger Operator on $H^s(\mathbb R^n). https://arxiv.org/abs/1912.09688

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