In this paper we study regularity of partial differential equations with polynomial coefficients in non isotropic Beurling spaces of ultradifferentiable functions of global type. We study the action of transformations of Gabor and Wigner type in such spaces and we prove that a suitable representation of Wigner type allows to prove regularity for classes of operators that do not have classical hypoellipticity properties.

中文翻译：

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非各向同性超微空间中偏微分方程整体解的时频规律

在本文中，我们研究了全局类型超微分函数的非各向同性Beurling空间中具有多项式系数的偏微分方程的正则性。我们研究了Gabor和Wigner型变换在此类空间中的作用，并证明了Wigner型的适当表示可以证明不具有经典次椭圆性的算子类别的正则性。