数苑讲座之一：Fractal Hardy space

发布时间：2021-09-17 作者：浏览次数：

Speaker:	董新汉	DateTime:	2021年9月20日（周一）下午2:30-3:30
Brief Introduction to Speaker: 董新汉教授，湖南师范大学。		Place:	6号楼二楼报告厅
Abstract:The first singular, non-atomic, spectral measure was constructed by Jorgensen and Pedersen. They proved that 1/R-Cantor measure $\mu_R$is a spectral measure with a spectrum $\Lambda$ if R is even。For any square integral function $f$, Let, $F_{f, \Lambda}=\sum_{\lambda\in\Lambda}f^(\lambda)z^{\lambda}$. Hence, H={F_{f, \Lambda}: f a is square integral function} is a complete subspace of Hardy space. In this talk, we mainly investigated the following problems: (1) Integral representation theorem of H; (2) Growth theorem of H；(3) Strichartz’s exceptional set and Carleson’s exceptional set under certain conditions;(4) Picard property, Cantor boundary behaviour of $F_{f,\Lambda}$, under Hadamard gap condition.