Given $n\geq2$ and $\alpha > \frac 12$, we obtained an improved upbound of Hausdorff's dimension of the fractional Schrödinger operator; that is, $$ \sup\limits_{f\in H^s(\mathbb{R}^n)}\dim _H\left\{x\in\mathbb{R}^n:\ \lim_{t\rightarrow0}e^{{\rm i}t(-\Delta)^\alpha}f(x)\neq f(x)\right\}\leq n+1-\frac{2(n+1)s}{n}%\ \ \text{under}\ \ \frac{n}{2(n+1)} < s\leq\frac{n}{2} $$ for $\frac{n}{2(n+1)} < s\leq\frac{n}{2}$.
Dan LI
,
Junfeng LI
,
Jie XIAO
. AN UPBOUND OF HAUSDORFF'S DIMENSION OF THE DIVERGENCE SET OF THE FRACTIONAL SCHRÖDINGER OPERATOR ON Hs($\mathbb{R}^n$)[J]. Acta mathematica scientia, Series B, 2021
, 41(4)
: 1223
-1249
.
DOI: 10.1007/s10473-021-0412-z
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