论文标题
部分可观测时空混沌系统的无模型预测
Coorbit theory of warped time-frequency systems in $\mathbb{R}^d$
论文作者
论文摘要
扭曲的时频系统最近作为一类结构化连续帧引入了实际线路上的功能。在此，我们将此框架推广到任意维度功能的设置。在证明扭曲的时频表示的基本特性将其延续到更高的维度之后，我们确定了翘曲函数的条件，该条件可以保证相关的Gramian已稳定化，以便可以构建相关的库里特空间家族。然后，我们证明可以通过对连续扭曲的时频系统进行采样来获得这些库里位空间的离散BANACH框架分解。特别是，这意味着在离散扭曲的时间频率词典中给定功能$ f $的稀疏性等同于Coorbit Space中的$ f $。我们特别强调了径向翘曲功能的情况，相关假设大大简化了这一功能。
Warped time-frequency systems have recently been introduced as a class of structured continuous frames for functions on the real line. Herein, we generalize this framework to the setting of functions of arbitrary dimensionality. After showing that the basic properties of warped time-frequency representations carry over to higher dimensions, we determine conditions on the warping function which guarantee that the associated Gramian is well-localized, so that associated families of coorbit spaces can be constructed. We then show that discrete Banach frame decompositions for these coorbit spaces can be obtained by sampling the continuous warped time-frequency systems. In particular, this implies that sparsity of a given function $f$ in the discrete warped time-frequency dictionary is equivalent to membership of $f$ in the coorbit space. We put special emphasis on the case of radial warping functions, for which the relevant assumptions simplify considerably.
