Micro-local analysis with Fourier Lebesgue spaces. I
type: Item
instance of: scholarly article
title: Micro-local analysis with Fourier Lebesgue spaces. I
zbMATH Open document ID: 1231.35329
author: Stevan Pilipović
author: Nenad Teofanov
author: Joachim Toft
published in: The Journal of Fourier Analysis and Applications
publication date: 2011-10-11T00:00:00Z
review text: The authors introduce wave-front sets of appropriate Banach (and Fréchet) spaces of tempered distributions, with special interest in the case in which these Banach spaces are weighted Fourier-Lebesgue type spaces. They show that their family of wave-front sets contains the classically known ones, and furthermore establish mapping properties on such wave-front sets for a quite general class of pseudodifferential operators. They show that the approach presented in this paper leads to a flexible microlocal tool which fits well in most commonly known approaches.
reviewed by: Alberto Parmeggiani
Mathematics Subject Classification ID: 35S30
Mathematics Subject Classification ID: 35A18
Mathematics Subject Classification ID: 47G30
Mathematics Subject Classification ID: 42B05
Mathematics Subject Classification ID: 42B37
zbMATH DE Number: 5956245
zbMATH Keywords: wave-front set
zbMATH Keywords: Fourier-Lebesgue space
zbMATH Keywords: modulation space
zbMATH Keywords: pseudodifferential operators
zbMATH Keywords: microlocal analysis
MaRDI profile type: Publication
full work available at URL: s00041-010-9138-1
OpenAlex ID: W2603386927
cites work: Q4112938
cites work: Global hypoellipticity and spectral theory
cites work: Time-frequency analysis of localization operators.
cites work: Pseudodifferential operators and Gabor frames: Spectral asymptotics
cites work: Q5451861
cites work: Banach spaces related to integrable group representations and their atomic decompositions. I
cites work: Banach spaces related to integrable group representations and their atomic decompositions. II
cites work: Gabor frames and time-frequency analysis of distributions
cites work: Harmonic Analysis in Phase Space. (AM-122)
cites work: Q2760042
cites work: Describing functions: Atomic decompositions versus frames
cites work: Foundations of time-frequency analysis
cites work: Modulation spaces and pseudodifferential operators
cites work: Weyl product algebras and modulation spaces
cites work: Lectures on nonlinear hyperbolic differential equations
cites work: Gabor pairs, and a discrete approach to wave-front sets
cites work: A Beurling-Helson type theorem for modulation spaces
cites work: On a symbol class of elliptic pseudodifferential operators
cites work: Pseudodifferential operators on ultra-modulation spaces.
cites work: Micro-local analysis in Fourier Lebesgue and modulation spaces. II
cites work: Pseudo-Differential Operators and Symmetries
cites work: Changes of variables in modulation and Wiener amalgam spaces
cites work: An algebra of pseudodifferential operators
cites work: The Boundedness of Pseudodifferential Operators on Modulation Spaces
cites work: Q5451866
cites work: Continuity properties for modulation spaces, with applications to pseudo-differential calculus. I.
cites work: Continuity properties for modulation spaces, with applications to pseudo-differential calculus. II
cites work: Continuity and Schatten Properties for Pseudo-differential Operators on Modulation Spaces
DOI: 10.1007/S00041-010-9138-1
description: scientific article; zbMATH DE number 5956245