Corpus ID: 227736661

Fredholm conditions for operators invariant with respect to compact Lie group actions.

@article{Baldare2020FredholmCF,
  title={Fredholm conditions for operators invariant with respect to compact Lie group actions.},
  author={Alexandre Baldare and R. Come and V. Nistor},
  journal={arXiv: Functional Analysis},
  year={2020}
}
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 two vector bundles $E_i \to M$, $i = 0,1$, and let $\alpha$ be an irreducible representation of the group $G$. 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. We prove that the map $\pi_\alpha(P)$ is Fredholm if, and… Expand

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