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arXiv · 1706.08413

The Gabor wave front set in spaces of ultradifferentiable functions

Chiara Boiti·David Jornet·Alessandro Oliaro
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Abstract

Given a non-quasianalytic subadditive weight function $\omega$ we consider the weighted Schwartz space $\mathcal{S}_\omega$ and the short-time Fourier transform on $\mathcal{S}_\omega$, $\mathcal{S}'_\omega$ and on the related modulation spaces with exponential weights. In this setting we define the $\omega$-wave front set $WF'_\omega(u)$ and the Gabor $\omega$-wave front set $WF^G_\omega(u)$ of $u\in\mathcal{S}'_{\omega}$, 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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Chiara Boiti, David Jornet, Alessandro Oliaro. 2017-06-26. The Gabor wave front set in spaces of ultradifferentiable functions. https://arxiv.org/abs/1706.08413

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