混合态局部化算子：Cohen类和迹族算子
Mixed-state localization operators: Cohen's class and trace class operators
摘要：
我们研究混合状态本地化运营商的角度沃纳的运营商卷积，使我们能够扩展已知的结果从秩一的情况下，迹族运营商。将信号定位到相空间中的一个域的思想从不同的方向进行了探讨，如扩散函数的界、与混合状态定位算子相关的概率密度、正算子值测度、正对应规则和算子平移的Tauberian定理的变体。我们的研究结果包括严格的治疗多窗口STFT滤波器和表征的混合状态本地化运营商作为积极的对应规则。此外，我们提供了一个描述的科恩类的维尔纳卷积的运营商和推导的后果，积极科恩类分布，不确定性原则，唯一性和相位检索的一般元素的科恩类。
英文摘要：
We study mixed-state localization operators from the perspective of Werner's operator convolutions which allows us to extend known results from the rank-one case to trace class operators. The idea of localizing a signal to a domain in phase space is approached from various directions such as bounds on the spreading function, probability densities associated to mixed-state localization operators, positive operator valued measures, positive correspondence rules and variants of Tauberian theorems for operator translates. Our results include a rigorous treatment of multiwindow-STFT filters and a characterization of mixed-state localization operators as positive correspondence rules. Furthermore, we provide a description of the Cohen class in terms of Werner's convolution of operators and deduce consequences on positive Cohen class distributions, an uncertainty principle, uniqueness and phase retrieval for general elements of Cohen's class.
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