Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 1135-1143 |
| Seitenumfang | 9 |
| Fachzeitschrift | Comptes rendus mathematique |
| Jahrgang | 359 |
| Ausgabenummer | 9 |
| Publikationsstatus | Veröffentlicht - 3 Nov. 2021 |
Abstract
Let G be a compact Lie group acting smoothly on a smooth, compact manifold M, let P ∈ ψm(M;E0,E1) be a G–invariant, classical pseudodifferential operator acting between sections of two G-equivariant vector bundles Ei → M, i = 0,1, and let α be an irreducible representation of the group G. Then P induces a map πα(P): Hs(M;E0)α → Hs−m(M;E1)α between the α-isotypical components. We prove that the map πα(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 Ei
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Allgemeine Mathematik
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in: Comptes rendus mathematique, Jahrgang 359, Nr. 9, 03.11.2021, S. 1135-1143.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
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TY - JOUR
T1 - Fredholm conditions for operators invariant with respect to compact Lie group actions
AU - Baldare, Alexandre
AU - Côme, Rémi
AU - Nistor, Victor
N1 - Funding Information: 2020 Mathematics Subject Classification. 47A53, 58J40, 57S15, 47L80, 46N20. Funding. A.B., R.C., and V.N. have been partially supported by ANR-14-CE25-0012-01 (SINGSTAR) . Manuscript received 7th December 2020, revised 25th March 2021 and 8th July 2021, accepted 10th August 2021.
PY - 2021/11/3
Y1 - 2021/11/3
N2 - Let G be a compact Lie group acting smoothly on a smooth, compact manifold M, let P ∈ ψm(M;E0,E1) be a G–invariant, classical pseudodifferential operator acting between sections of two G-equivariant vector bundles Ei → M, i = 0,1, and let α be an irreducible representation of the group G. Then P induces a map πα(P): Hs(M;E0)α → Hs−m(M;E1)α between the α-isotypical components. We prove that the map πα(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 Ei
AB - Let G be a compact Lie group acting smoothly on a smooth, compact manifold M, let P ∈ ψm(M;E0,E1) be a G–invariant, classical pseudodifferential operator acting between sections of two G-equivariant vector bundles Ei → M, i = 0,1, and let α be an irreducible representation of the group G. Then P induces a map πα(P): Hs(M;E0)α → Hs−m(M;E1)α between the α-isotypical components. We prove that the map πα(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 Ei
UR - http://www.scopus.com/inward/record.url?scp=85119906611&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2012.03944
DO - 10.48550/arXiv.2012.03944
M3 - Article
AN - SCOPUS:85119906611
VL - 359
SP - 1135
EP - 1143
JO - Comptes rendus mathematique
JF - Comptes rendus mathematique
SN - 1631-073X
IS - 9
ER -