论文标题
从正面科恩的班级分布中的调制空间的同等规范
Equivalent norms for modulation spaces from positive Cohen's class distributions
论文作者
论文摘要
我们通过由Hilbert-Schmidt操作员替换短期傅立叶变换的窗口，为调制空间提供新的等效规范。主要结果应用于Cohen的时间频率分布，Weyl操作员和本地化操作员。特别是，任何与Schwartz内核的积极的Cohen类别分布都可以用于为调制空间提供等效的规范。我们还获得了调制空间作为时频Wiener amalgam空间的描述。希尔伯特·史克米特（Hilbert-Schmidt）操作员必须满足这些结果的核条件，我们将详细研究这种情况。
We give a new class of equivalent norms for modulation spaces by replacing the window of the short-time Fourier transform by a Hilbert-Schmidt operator. The main result is applied to Cohen's class of time-frequency distributions, Weyl operators and localization operators. In particular, any positive Cohen's class distribution with Schwartz kernel can be used to give an equivalent norm for modulation spaces. We also obtain a description of modulation spaces as time-frequency Wiener amalgam spaces. The Hilbert-Schmidt operator must satisfy a nuclearity condition for these results to hold, and we investigate this condition in detail.
