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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 ofExpand
Analysis on singular spaces and index theory
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 operatorExpand
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 twoExpand
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 , iExpand
Gluing action groupoids: differential operators and Fredholm conditions
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
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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
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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 actionExpand
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The Fredholm property for groupoids is a local property
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 ofExpand
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