Operators on manifolds with conical singularities
type: Item
instance of: scholarly article
title: Operators on manifolds with conical singularities
zbMATH Open document ID: 1205.35354
author: Li Ma
author: B.-W. Schulze
published in: Journal of Pseudo-Differential Operators and Applications
publication date: 2010-11-03T00:00:00Z
full work available at URL: urn:nbn:de:kobv:517-opus-36608
review text: The authors consider general nature of pseudo-differential algebras on a manifold with conical or edge singularities of order 1. The presence of symbolic hierarchies is a new aspect, compared with the smooth case. Ellipticity of an operator \(A\) on such space is a bijectivity condition on a principal symbolic hierarchy \((\sigma_0,\sigma_1)\) where \(\sigma_0\) is the standard degenerate homogeneous principal symbol, and \(\sigma_1\) is the so-called conormal symbol. They show the existence of a smoothing Mellin operator \(F\) belonging to the cone algebra such that \(A+F\) is also elliptic with respect to \(\sigma_1\) for a prescribed weight \(\gamma\in\mathbb{R}\). This result considerably simplifies the parametrix construction in the cone algebra.
reviewed by: Rémi Vaillancourt
Mathematics Subject Classification ID: 35S35
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 47G30
Mathematics Subject Classification ID: 58J40
zbMATH DE Number: 5809988
zbMATH Keywords: operators on manifolds with conical singularities
zbMATH Keywords: conormal symbols
zbMATH Keywords: ellipticity of cone operators
zbMATH Keywords: parametrices and invertibility within the cone calculus
MaRDI profile type: Publication
OpenAlex ID: W2007387851
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DOI: 10.1007/S11868-010-0002-5
description: scientific article; zbMATH DE number 5809988