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Fredholm conditions for operators invariant with respect to compact Lie group actions.
Let $G$ be a compact Lie group acting smoothly on a smooth, compact manifold $M$, let $P \in \psi^m(M; E_0, E_1)$ be a $G$--invariant, classical pseudodifferential operator acting between sections of… Expand
Analysis on singular spaces and index theory
- R. Come
- 26 June 2020
This thesis is set in the general context of extending the theory of elliptic operators, well-understood in the smooth setting, to so-called singular domains. The methods used rely on operator… Expand
Fredholm conditions and index for restrictions of invariant pseudodifferential operators to isotypical components
Let $\Gamma$ be a finite group acting on a smooth, compact manifold $M$, let $P \in \psi^m(M; E_0, E_1)$ be a $\Gamma$-invariant, classical pseudodifferential operator acting between sections of two… Expand
Fredholm conditions for restrictions of invariant pseudodifferential operators to isotypical components
Let Γ be a finite group acting on a smooth, compact manifold M , let P ∈ ψ(M ;E0, E1) be a Γ-invariant, classical pseudodifferential operator acting between sections of two vector bundles Ei → M , i… Expand
Gluing action groupoids: differential operators and Fredholm conditions
- R. Come
- 4 August 2018
We prove some Fredholm conditions for many algebras of differential operators on particular classes of open manifolds, which include asymptotically Euclidean or asymptotically hyperbolic manifolds.… Expand
Fredholm conditions for invariant operators: finite abelian groups and boundary value problems
We answer the question of when an invariant pseudodifferential operator is Fredholm on a fixed, given isotypical component. More precisely, let $\Gamma$ be a compact group acting on a smooth,… Expand
Gluing action groupoids: Fredholm conditions and layer potentials.
This paper is a merge of arXiv:1807.05418 and arXiv:1808.01442. We introduce a new class of groupoids, called "boundary action groupoids", which are obtained by gluing reductions of action… Expand
The Fredholm property for groupoids is a local property
- R. Come
- 15 October 2018
Fredholm Lie groupoids were introduced by Carvalho, Nistor and Qiao as a tool for the study of partial differential equations on open manifolds. This article extends the definition to the setting of… Expand