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数苑博雅讲座
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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
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.

董新汉 教授, 湖南师范大学。