On the resolvent of differential operators on conic manifolds
type: Item
instance of: scholarly article
title: On the resolvent of differential operators on conic manifolds
zbMATH Open document ID: 1038.58031
author: Paul Loya
published in: Communications in Analysis and Geometry
publication date: 2003-10-13T00:00:00Z
review text: The aim of the paper is to describe the structure of resolvent of a cone differential operator acting between weighted Sobolev spaces on a compact manifold with boundary \(X\). It is proved that if \(A\) is a cone differential operator of order \(m\), fully elliptic with respect to \(\alpha\in {\mathbb R}\) on a close sector \(\Lambda\), then \((A-\lambda)^{-1}\) is \(b\)-pseudodifferential, \(\lambda\mapsto (A-\lambda)^{-1}\) is meromorphic having only finite rank singularities. Moreover a precise description of the asymptotic are given as the spectral parameter \(\lambda\) tends to zero. It is shown how the singularities of the Schwartz kernel of \((A-\lambda)^{-1}\) accumulate near diagonal as \(\lambda\rightarrow \infty\). A trace formula for the operator \(B(A-\lambda)^{-N}\) is given, where \(B\) is a cone differential operator.
reviewed by: Leszek Skrzypczak
Mathematics Subject Classification ID: 58J37
Mathematics Subject Classification ID: 58J40
zbMATH DE Number: 1925892
zbMATH Keywords: cone differential operators
zbMATH Keywords: elliptic operators
zbMATH Keywords: manifolds with corners
Wikidata QID: Q115205525
MaRDI profile type: Publication
DOI: 10.4310/CAG.2002.V10.N5.A1
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description: scientific article; zbMATH DE number 1925892