Micro-local analysis in some spaces of ultradistributions

2011/09/24 by Karoline Johansson, Stevan Pilipović, Johansson, Karoline +5
Computer Science · Engineering · Mathematics · #35A18 #35H10 #35S30 #42B05 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1109.5250

openalex publication_date 2011/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we extend some results from our earlier papers on wave-front sets, concerning wave-front sets of Fourier-Lebesgue and modulation space types, to a broader class of spaces of ultradistributions, and relate these wave-front sets with the usual wave-front sets of ultradistributions. Furthermore, we use Gabor frames for the description of discrete wave-front sets, and prove that these wave-front sets coincide with corresponding continuous ones.

Related

• Wave front sets with respect to Banach spaces of ultradistributions.\n Characterisation via the short-time Fourier transform
• Discrete Wave-front sets of Fourier Lebesgue and modulation space types
• Microlocal analysis of quasianalytic Gelfand-Shilov type\n ultradistributions
• Micro-local analysis in Fourier Lebesgue and modulation spaces. Part I
• Micro-local analysis in Fourier Lebesgue and modulation spaces. Part II