论文标题
部分可观测时空混沌系统的无模型预测
A Rudin--de Leeuw type theorem for functions with spectral gaps
论文作者
论文摘要
我们的起点是De Leeuw和Rudin的定理，它描述了Hardy Space $ H^1 $中单元球的极端点。我们将此结果扩展到$ h^1 $的子空间，该子空间由具有较小光谱的函数形成。 More precisely, given a finite set $\mathcal K$ of positive integers, we prove a Rudin--de Leeuw type theorem for the unit ball of $H^1_{\mathcal K}$, the space of functions $f\in H^1$ whose Fourier coefficients $\widehat f(k)$ vanish for all $k\in\mathcal K$.
Our starting point is a theorem of de Leeuw and Rudin that describes the extreme points of the unit ball in the Hardy space $H^1$. We extend this result to subspaces of $H^1$ formed by functions with smaller spectra. More precisely, given a finite set $\mathcal K$ of positive integers, we prove a Rudin--de Leeuw type theorem for the unit ball of $H^1_{\mathcal K}$, the space of functions $f\in H^1$ whose Fourier coefficients $\widehat f(k)$ vanish for all $k\in\mathcal K$.
