On the second microlocalization along isotropic submanifolds
type: Item
instance of: scholarly article
title: On the second microlocalization along isotropic submanifolds
zbMATH Open document ID: 0810.32018
author: Kiyoshi Takeuchi
published in: Proceedings of the Japan Academy. Series A
publication date: 1995-04-04T00:00:00Z
review text: The author's summary: ``Around 1985, Lebeau developed the theory of the theory of the second microlocalisation along isotropic submanifolds, and defined the ``\(\Gamma\)-analytic microfunction'' that had the unique continuation properties along bicharacteristic leaves. In this paper the author gives an explicit representation using the boundary values of holomorphic functions as \textit{Y. Okada} and \textit{N. Tose} did [see J. Math. Pures Appl., IX. Ser. 70, No. 4, 427-453 (1991; Zbl 0771.35003)] in the case of regular involutive submanifolds. The author proves that ``\(\Gamma\)-analytic microfunctions'' form a strictly wider subclass of the micro-functions than that of microfunctions with holomorphic parameters. The author proves other results, too. Note that the author's methods of proof are completely different from Lebeau's.
Mathematics Subject Classification ID: 32S99
Mathematics Subject Classification ID: 35A27
Mathematics Subject Classification ID: 58J15
zbMATH DE Number: 559497
zbMATH Keywords: co-isotropy
zbMATH Keywords: FBI-transformation
zbMATH Keywords: second microlocalisation
zbMATH Keywords: isotropic submanifolds
zbMATH Keywords: micro-functions
MaRDI profile type: Publication
full work available at URL: pjaa.69.136
OpenAlex ID: W2002502721
cites work: Q4104280
cites work: Q4112844
cites work: Propagation des singularités analytiques pour les solutions des équations aux derivées partielles
cites work: Q3717382
cites work: Q3697337
cites work: Q5651000
cites work: Deuxième microlocalisation sur les sous variétés isotropes
cites work: FBI transformation and second microlocalization equivalence of second analytic wave front sets and second singular spectrums
cites work: Q4403324
cites work: Q3037865
DOI: 10.3792/PJAA.69.136
description: scientific article; zbMATH DE number 559497