Singular integral operators on non-compact manifolds and analysis on polyhedral domains
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arXiv
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| Format: | Preprint |
| Publié: |
2004
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| _version_ | 1866918162925092864 |
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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 |