Micro-local analysis in some spaces of ultradistributions

Abstract

We extend some results from [14] and [19], concerning wave-front sets of Fourier-Lebesgue and modulation space types, to a broader class of spaces of ultradistributions. We relate these wave-front sets one to another and to the usual wave-front sets of ultradistributions. Furthermore, we give a description of discrete wave-front sets by introducing the notion of discretely regular points, and prove that these wave-front sets coincide with corresponding wave-front sets in [19]. Some of these investigations are based on the properties of the Gabor frames.