On an isomorphism of the algebra of pseudo-differential operators
type: Item
instance of: scholarly article
title: On an isomorphism of the algebra of pseudo-differential operators
zbMATH Open document ID: 0552.58029
published in: Journal of Mathematics of Kyoto University
publication date: 1984-01-01T00:00:00Z
review text: On the basis of a previous result by \textit{J. J. Duistermaat} and \textit{I. M. Singer} [Commun. Pure Appl. Math. 29, 39-47 (1976; Zbl 0317.58017)], the following theorem is proved. Let M be a compact connected smooth manifold, and \(\alpha\) an automorphism of the algebra of all pseudodifferential operators on M; assuming that (i) the two-sided ideal of operators with smooth kernel is globally invariant under \(\alpha\), and (ii) \(\alpha\) maps vector fields into vector fields, then \(\alpha\) is the isomorphism naturally defined by a (unique) diffeomorphism of M onto itself.
Mathematics Subject Classification ID: 58J40
Mathematics Subject Classification ID: 47Gxx
Mathematics Subject Classification ID: 35S05
zbMATH DE Number: 3879777
zbMATH Keywords: Fourier integral operators
zbMATH Keywords: pseudodifferential operators
author: Kenro Furutani
reviewed by: François Rouvière
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250521329
OpenAlex ID: W1602742485
DOI: 10.1215/KJM/1250521329
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description: scientific article; zbMATH DE number 3879777