The Gabor wave front set in spaces of ultradifferentiable functions

2017/06/26 by Boiti, Chiara, Jornet, David, Oliaro, Alessandro · 1 citation
#35S05 #42C15 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 35A18 #Secondary 46F05

paper · doi:10.48550/arxiv.1706.08413

Abstract

Given a non-quasianalytic subadditive weight function ω we consider the weighted Schwartz space S_ω and the short-time Fourier transform on S_ω, 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\inS'_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.

Cited by

• Composition operators on weighted modulation spaces

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