Spectral Cantor-Moran measures and a Bourgain Sum of Sine problem

发布时间：2019-06-21 来源：赢咖3 浏览次数：

Speaker:	赖俊杰（Lai Chun-kit）	DateTime:	2019年6月25日（周二）上午10:00-12:00
Brief Introduction to Speaker: 赖俊杰（Lai Chun-kit）,美国旧金山州立大学。		Place:	六号楼二楼报告厅
Abstract: Let $\{(N_n,B_n,L_n)\}$ with $B_n\subset \{0,1,..,N_n-1\}$ for $n=1,2,...$ be a sequence of Hadamard triples, we will show that, except an extreme case, the associated Cantor-Moran measure $$\mu = \mu(N_n,B_n) = \delta_{\frac{1}{N_1}B_1}\ast\delta_{\frac{1}{N_1N_2}B_2}\ast\delta_{\frac{1}{N_1N_2N_3}B_3}\ast...\\$$ with support inside $[0,1]$ always admits an exponential orthonormal basis $E(\Lambda) = \{e^{2\pi i \lambda x}:\lambda\in\Lambda\}$ for $L^2(\mu)$, where $\Lambda$ is obtained from suitably modifying $L_n$. In the extreme case, we show that its spectality is related to the ''Bourgain Sum of Sine problem''. This is a joint work with L-X An and X.-Y Fu.