Singular integral operators on non-compact manifolds and analysis on polyhedral domains

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1. Verfasser: Nistor, Victor
Format: Preprint
Veröffentlicht: 2004
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author Nistor, Victor
author_facet Nistor, Victor
contents We review the definition of a Lie manifold $(M, \VV)$ and the construction of the algebra $Ψ\sp{\infty}\sb{\VV}(M)$ of pseudodifferential operators on a Lie manifold $(M, \VV)$. We give some concrete Fredholmness conditions for pseudodifferential operators in $Ψ\sp{\infty}\sb{\VV}(M)$ for a large class of Lie manifolds $(M, \VV)$. These Fredholmness conditions have applications to boundary value problems on polyhedral domains and to non-linear PDEs on non-compact manifolds. As an application, we determine the spectrum of the Dirac operator on a manifold with multi-cylindrical ends.
format Preprint
id arxiv_https___arxiv_org_abs_math_0402322
institution arXiv
publishDate 2004
record_format arxiv
spellingShingle Singular integral operators on non-compact manifolds and analysis on polyhedral domains
Nistor, Victor
Analysis of PDEs
Numerical Analysis
Spectral Theory
We review the definition of a Lie manifold $(M, \VV)$ and the construction of the algebra $Ψ\sp{\infty}\sb{\VV}(M)$ of pseudodifferential operators on a Lie manifold $(M, \VV)$. We give some concrete Fredholmness conditions for pseudodifferential operators in $Ψ\sp{\infty}\sb{\VV}(M)$ for a large class of Lie manifolds $(M, \VV)$. These Fredholmness conditions have applications to boundary value problems on polyhedral domains and to non-linear PDEs on non-compact manifolds. As an application, we determine the spectrum of the Dirac operator on a manifold with multi-cylindrical ends.
title Singular integral operators on non-compact manifolds and analysis on polyhedral domains
topic Analysis of PDEs
Numerical Analysis
Spectral Theory
url https://arxiv.org/abs/math/0402322