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Théorie de l'indice pour les familles d'opérateurs G-transversalement elliptiques
Le probleme de l'indice est de calculer l'indice d'un operateur elliptique en termes topologiques. Ce probleme fut resolu par M. Atiyah et I. Singer en 1963 dans "The index of elliptic operators onExpand
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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
The index of G-transversally elliptic families in KK-theory
We define and study the index map for families of G-transversally elliptic operators and introduce the multiplicity for a given irreducible representation as a virtual bundle over the base of theExpand
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The index of leafwise G-transversally elliptic operators on foliations
We introduce and study the index morphism for G-invariant leafwise G-transversally elliptic operators on smooth closed foliated manifolds which are endowed with leafwise actions of the compact groupExpand
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The index of G-transversally elliptic families II
We define the Chern character of the index class of a $G$-invariant family of $G$-transversally elliptic operators, see [6]. Next we study the Berline-Vergne formula for families in the elliptic andExpand
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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
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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The index of G-transversally elliptic families in cohomology.
We define the Chern character of the index class of a $G$-invariant family of $G$-transversally elliptic operators, see [6]. Next we study the Berline-Vergne formula for families in the elliptic andExpand
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