Corpus ID: 211249125

Fredholm conditions for restrictions of invariant pseudodifferential operators to isotypical components

@inproceedings{Baldare2020FredholmCF,
  title={Fredholm conditions for restrictions of invariant pseudodifferential operators to isotypical components},
  author={Alexandre Baldare and R. Come and M. Lesch and V. Nistor},
  year={2020}
}
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 = 0, 1, and let α be an irreducible representation of the group Γ. Then P induces a map πα(P ) : H (M ;E0)α → Hs−m(M ;E1)α between the α-isotypical components of the corresponding Sobolev spaces of sections. We prove that the map πα(P ) is Fredholm if, and only if, P is α-elliptic, a condition… Expand

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