Micro-local analysis in Fourier Lebesgue and modulation spaces. Part I

2008/04/10 by Stevan Pilipović, Stevan Pilipovic, Pilipovic, Stevan +4
Computer Science · Earth and Planetary Sciences · Mathematics · #35A18 #35Sxx #42B35 #47G30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Seismic Imaging and Inversion Techniques #math.AP #math.FA #msc:35A18 #msc:35Sxx #msc:42B35 #msc:47G30

paper · pdf · doi:10.48550/arxiv.0804.1730

openalex publication_date 2008/04/10 · arxiv created 2009/11/25 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let ω,ω₀ be appropriate weight functions and q∈ [1,∞ ]. We introduce the wave-front set, \WF_\mathscr FL^q_(ω)(f) of f∈ \mathscr S' with respect to weighted Fourier Lebesgue space \mathscr FL^q_(ω). We prove that usual mapping properties for pseudo-differential operators \op (a) with symbols a in S^(ω₀)_{ρ, 0} hold for such wave-front sets. Especially we prove \WF_\mathscr FL^q_(ω/ω0)(\op (a)f)⊆ \WF_\mathscr FL^q_(ω)(f) ⊆ \WF_\mathscr FL^q_(ω/ω0)(\op (a)f)\ttbigcup \Char (a). %% Here \Char (a) is the set of characteristic points of a.

Citations

• Pseudodifferential operators and Banach algebras in mobile communications
• A Beurling-Helson type theorem for modulation spaces

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