超可微函数空间中的Gabor波前集
The Gabor wave front set in spaces of ultradifferentiable functions
摘要：
给定一个非拟解析次可加权函数$ω$，我们考虑加权施瓦兹空间$\mathcal{S}_ω$和在$\mathcal{S}_ω$，$\mathcal{S}'_ω$及相关的指数权调制空间上的短时傅里叶变换.在这种情况下，我们定义的$ω$ -波前集$WF'_ω(u)$和Gabor $ω$ -波前集$WF^G_ω(u)$的$u\in\mathcal{S}'_ω$，我们证明，他们是一致的。最后，我们看看这个波前集的微分和伪微分型运营商的应用。
英文摘要：
Given a non-quasianalytic subadditive weight function $ω$ we consider the weighted Schwartz space $\mathcal{S}_ω$ and the short-time Fourier transform on $\mathcal{S}_ω$, $\mathcal{S}'_ω$ and on the related modulation spaces with exponential weights. In this setting we define the $ω$-wave front set $WF'_ω(u)$ and the Gabor $ω$-wave front set $WF^G_ω(u)$ of $u\in\mathcal{S}'_ω$, and we prove that they coincide. Finally we look at applications of this wave front set for operators of differential and pseudo-differential type.
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