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Comptes Rendus. Mathématique
Operator theory
Fredholm conditions for operators invariant with respect to compact Lie group actions
Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1135-1143.

Let G be a compact Lie group acting smoothly on a smooth, compact manifold M, let Pψ m (M;E 0 ,E 1 ) be a G–invariant, classical pseudodifferential operator acting between sections of two G-equivariant vector bundles E i M, i=0,1, and let α be an irreducible representation of the group G. Then P induces a map π α (P):H s (M;E 0 ) α H s-m (M;E 1 ) α between the α-isotypical components. We prove that the map π α (P) is Fredholm if, and only if, P is transversally α-elliptic, a condition defined in terms of the principal symbol of P and the action of G on the vector bundles E i .

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DOI: 10.5802/crmath.257
Classification: 47A53,  58J40,  57S15,  47L80,  46N20
Alexandre Baldare 1; Rémi Côme 2; Victor Nistor 2

1 Institut fur Analysis, Welfengarten 1, 30167 Hannover, Germany
2 Université Lorraine, 57000 Metz, France
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     title = {Fredholm conditions for operators invariant with respect to compact {Lie} group actions},
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Alexandre Baldare; Rémi Côme; Victor Nistor. Fredholm conditions for operators invariant with respect to compact Lie group actions. Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1135-1143. doi : 10.5802/crmath.257. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.257/

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