Recently we introduced mixed-state localization operators associated with a density operator and a (compact) domain in phase space. We continue the investigations of their eigenvalues and eigenvectors. Our main focus is the definition of a time-frequency distribution that is based on the Cohen class distribution associated with the density operator and the eigenvectors of the mixed-state localization operator. This time-frequency distribution is called the accumulated Cohen class distribution. If the trace class operator is a rank-one operator, then the mixed-state localization operators and the accumulated Cohen class distribution reduce to Daubechies’ localization operators and the accumulated spectrogram. We extend all the results about the accumulated spectrogram to the accumulated Cohen class distribution. The techniques used in the case of spectrograms cannot be adapted to other distributions in Cohen’s class since they rely on the reproducing kernel property of the short-time Fourier transform. Our approach is based on quantum harmonic analysis on phase space, which also provides the tools and notions to introduce the analogues of the accumulated spectrogram for mixed-state localization operators, the accumulated Cohen’s class distributions.

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关于累积 Cohen 类分布和混合状态定位算子

最近我们引入了与密度算子和相空间中的（紧凑）域相关的混合状态定位算子。我们继续研究它们的特征值和特征向量。我们的主要重点是时频分布的定义，该分布基于与密度算子和混合状态定位算子的特征向量相关的 Cohen 类分布。这种时频分布称为累积 Cohen 类分布。如果迹类算子是一阶算子，则混合状态定位算子和累积的 Cohen 类分布简化为 Daubechies 的定位算子和累积的谱图。我们将所有关于累积谱图的结果扩展到累积的 Cohen 类分布。在频谱图的情况下使用的技术不能适用于 Cohen 类中的其他分布，因为它们依赖于短时傅立叶变换的再现核特性。我们的方法基于相空间上的量子谐波分析，它还提供了工具和概念来引入混合状态定位算子的累积谱图的类似物，即累积的 Cohen 类分布。