Wigner变换的线性微扰与Weyl量子化
Linear perturbations of the Wigner transform and the Weyl quantization
摘要：
我们研究一类二次时频表示，粗略地说，是通过线性扰动的维格纳变换。它们在默认情况下满足Moyal公式，并与Wigner变换共享许多其他性质，但通常它们不属于Cohen的类。我们提供了两个类的交集的表征。对于任何这样的时间-频率表示，我们关联一个伪微分。我们研究了相关的量子化过程，研究了伪微分算子的性质，并与Weyl演算的形式主义进行了比较。
英文摘要：
We study a class of quadratic time-frequency representations that, roughly speaking, are obtained by linear perturbations of the Wigner transform. They satisfy Moyal's formula by default and share many other properties with the Wigner transform, but in general they do not belong to Cohen's class. We provide a characterization of the intersection of the two classes. To any such time-frequency representation, we associate a pseudodifferential calculus. We investigate the related quantization procedure, study the properties of the pseudodifferential operators, and compare the formalism with that of the Weyl calculus.
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