The FBI transforms and their use in microlocal analysis
type: Item
instance of: scholarly article
title: The FBI transforms and their use in microlocal analysis
zbMATH Open document ID: 1395.35007
author: R. Medrado
author: Gustavo Hoepfner
published in: Journal of Functional Analysis
publication date: 2018-06-20T00:00:00Z
review text: In the paper under review, certain problems of microlocal analysis are studied. This topic deals with smooth microlocal singularities (the collection of directions in which the Fourier transform does not decay rapidly), the set of which is called a smooth wave front set. Using a more general class of FBI transforms, introduced by S. Berhanu and J. Hounie, the authors completely characterize regularity and microregularity in Denjoy-Carleman (non-quasi-analytic) classes, which includes the Gevrey classes and M. Christ version of the FBI transform as examples. They also exhibit a result on microlocal regularity for solutions of first order partial differential equations in these classes, that do not seem possible to prove using the classical FBI transform.
reviewed by: Elijah Liflyand
Mathematics Subject Classification ID: 35A27
Mathematics Subject Classification ID: 42B10
Mathematics Subject Classification ID: 35A18
Mathematics Subject Classification ID: 35A21
Mathematics Subject Classification ID: 35A22
Mathematics Subject Classification ID: 35N10
zbMATH DE Number: 6891995
zbMATH Keywords: Fourier transform
zbMATH Keywords: smooth microlocal singularities
zbMATH Keywords: Gevrey classes
MaRDI profile type: Publication
full work available at URL: j.jfa.2018.05.022
OpenAlex ID: W2808021753
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Wikidata QID: Q129654653
DOI: 10.1016/J.JFA.2018.05.022
description: scientific article; zbMATH DE number 6891995