Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2004
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/math/0402322 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of 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.