Invariance of the cone algebra without asymptotics
type: Item
instance of: scholarly article
title: Invariance of the cone algebra without asymptotics
zbMATH Open document ID: 0865.58045
DOI: 10.1007/BF00129899
author: Elmar Schrohe
published in: Annals of Global Analysis and Geometry
publication date: 1997-07-13T00:00:00Z
review text: The author considers a cone algebra of Mellin operators defined on a manifold with conical singularities. Let the manifold be the cylinder \(X\times \overline{\mathbb{R}}_+\), where \(X\) is a compact smooth manifold without boundary. Then the Mellin operator has a symbol that is a smooth function on \(\mathbb{R}_+\times \mathbb{R}_+\) with values in an algebra of pseudodifferential operators on \(X\). The main result of the paper is the invariance of this cone algebra under smooth change of variables \((x,t)\to(\chi(x,t),\sigma(x,t))\) in the cylinder \(X\times \overline{\mathbb{R}}_+\).
Mathematics Subject Classification ID: 58J40
Mathematics Subject Classification ID: 47L30
Mathematics Subject Classification ID: 46H35
zbMATH DE Number: 955342
zbMATH Keywords: manifold with conical singularities
zbMATH Keywords: Mellin operator
zbMATH Keywords: pseudodifferential operators
reviewed by: Georgi E. Karadzhov
MaRDI profile type: Publication
cites work: Q3917198
cites work: Pseudodifferential operators of mellin type
cites work: Transformation of boundary problems
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cites work: Complete Mellin and Green symbolic calculus in spaces with conormal asymptotics
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cites work: Mellin representations of pseudo-differential operators on manifolds with corners
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description: scientific article; zbMATH DE number 955342