Singular integral operators on non-compact manifolds and analysis on polyhedral domains
arXiv:math/0402322
Abstract
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.
19 pages, AMS-LaTeX