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

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

2004-02-19

arxiv.org/abs/math/0402322v1

Mathematics

Analysis of PDEs

19 pages, AMS-LaTeX

Scientific paper

We review the definition of a Lie manifold $(M, \VV)$ and the construction of the algebra $\Psi\sp{\infty}\sb{\VV}(M)$ of pseudodifferential operators on a Lie manifold $(M, \VV)$. We give some concrete Fredholmness conditions for pseudodifferential operators in $\Psi\sp{\infty}\sb{\VV}(M)$ 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.

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