论文标题
调制空间的操作员窗口上的注释
A note on the operator window of modulation spaces
论文作者
论文摘要
受到最近一篇文章\ Cite [JFAA，28（2）：1-34，（2022）] {skrettingland20222jofaaa}的启发，本文致力于在$ l^2（\ rd）上的有限线性操作员框架中研究合适的窗口类。我们为窗口类建立了自然而完整的表征，以使相应的STFT导致调制空间的等效规范。在Cohen的类别分布中也表征了正结合的线性运算符，因此相应的数量构成了调制空间的等效规范。作为概括，我们介绍了与操作员值调制空间相对应的操作员类。我们的主要定理对本地化运营商的某些应用也涉及。
Inspired by a recent article \cite[JFAA, 28(2):1-34, (2022)]{Skrettingland2022JoFAaA}, this paper is devoted to the study of suitable window class in the framework of bounded linear operators on $L^2(\rd)$. We establish a natural and complete characterization for the window class such that the corresponding STFT leads to equivalent norms of modulation spaces. The positive bounded linear operators are also characterized in Cohen's class distributions such that the corresponding quantities form equivalent norms of modulation spaces. As a generalization, we introduce a family of operator classes corresponding to the operator-valued modulation spaces. Some applications of our main theorems to the localization operators are also concerned.
