Corpus ID: 214795382

Fredholm conditions and index for restrictions of invariant pseudodifferential operators to isotypical components

@article{Baldare2020FredholmCA,
  title={Fredholm conditions and index for restrictions of invariant pseudodifferential operators to isotypical components},
  author={Alexandre Baldare and R. Come and M. Lesch and V. Nistor},
  journal={arXiv: Differential Geometry},
  year={2020}
}
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 equivariant vector bundles $E_i \to M$, $i = 0,1$, and let $\alpha$ be an irreducible representation of the group $\Gamma$. Then $P$ induces a map $\pi_\alpha(P) : H^s(M; E_0)_\alpha \to H^{s-m}(M; E_1)_\alpha$ between the $\alpha$-isotypical components of the corresponding Sobolev spaces of… Expand

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