A Lie group structure for pseudodifferential operators
type: Item
instance of: scholarly article
title: A Lie group structure for pseudodifferential operators
zbMATH Open document ID: 0587.58047
DOI: 10.1007/BF01472130
author: R. Schmid
author: Malcolm R. Adams
author: T. S. Ratiu
published in: Mathematische Annalen
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164072
review text: The work consists of five sections. Section 1 is introductory. In section 2 the spaces of formal pseudodifferential operators and Fourier integral operators on a compact manifold M are described. In section 3 the basic facts on ILH (inverse limit Hilbert) Lie groups are reviewed and the ILH group structure for \(D_{\theta}(T^*M\setminus 0)\) are constructed, where \(D_{\theta}(T^*M\setminus 0)\) is the space of smooth diffeomorphisms of \(T^*M\setminus 0\) which preserve the canonical one- form \(\theta\) on \(T^*M\). In section 4 a global phase function for all \(\theta\)-preserving diffeomorphisms of \(T^*M\setminus 0\) which are \(C^ 1\)-close to the identity are constructed. This gives a global writing for invertible Fourier integral operators with canonical relation close to the identity. In section 5 the differentiable structure on invertible, order zero, formal pseudodifferential operators are introduced.
reviewed by: Sattor Baĭzaev
Mathematics Subject Classification ID: 58J40
zbMATH DE Number: 3942572
zbMATH Keywords: pseudodifferential and Fourier integral operators on manifolds
Wikidata QID: Q115393399
MaRDI profile type: Publication
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OpenAlex ID: W2088210355
description: scientific article; zbMATH DE number 3942572