On covariant functions and distributions under the action of a compact group
| dc.creator | Saidi, Anouar | |
| dc.date | 2009-02-09 | |
| dc.date.accessioned | 2026-07-07T12:39:25Z | |
| dc.date.available | 2026-07-07T12:39:25Z | |
| dc.description | Let $G$ be a compact subgroup of $GL_n(\R)$ acting linearly on a finite dimensional vector space $E$. B. Malgrange has shown that the space $\mathcal{C}^\infty(\R^n,E)^G$ of $\mathcal{C}^\infty$ and $G$-covariant functions is a finite module over the ring $\mathcal{C}^\infty(\R^n)^G$ of $\mathcal{C}^\infty$ and $G$-invariant functions. First, we generalize this result for the Schwartz space $\mathscr{S}(\R^n,E)^G$ of $G$-covariant functions. Secondly, we prove that any $G$-covariant distribution can be decomposed into a sum of $G$-invariant distributions multiplied with a fixed family of $G$-covariant polynomials. This gives a generalization of an Oksak result proved in ([O]). | |
| dc.identifier | https://arxiv.org/abs/0902.1383 | |
| dc.identifier | http://arxiv.org/abs/0902.1383 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/219102 | |
| dc.subject | Representation Theory | |
| dc.subject | 46F05; 58C99; 58C81; 58C46. | |
| dc.title | On covariant functions and distributions under the action of a compact group | |
| dc.type | text |