Homomorphisms of infinitely generated analytic sheaves
| dc.creator | Masagutov, Vakhid | |
| dc.date | 2008-11-12 | |
| dc.date.accessioned | 2026-07-07T10:17:46Z | |
| dc.date.available | 2026-07-07T10:17:46Z | |
| dc.description | We prove that every homomorphism $\mathcal{O}^E_ζ\to\mathcal{O}^F_ζ$, with $E$ and $F$ Banach spaces and $ζ\in\mathbb{C}^m$, is induced by a $\mathop{\mathrm{Hom}}(E,F)$-valued holomorphic germ, provided that $1\leq m<\infty$. A similar structure theorem is obtained for the homomorphisms of type $\mathcal{O}^E_ζ\to\mathcal{S}_ζ$, where $\mathcal{S}_ζ$ is a stalk of a coherent sheaf of positive $\mathfrak{m}_ζ$-depth. We later extend these results to sheaf homomorphisms, obtaining a condition on coherent sheaves which guarantees the sheaf to be equipped with a unique analytic structure in the sense of Lempert-Patyi. | |
| dc.identifier | https://arxiv.org/abs/0811.1978 | |
| dc.identifier | http://arxiv.org/abs/0811.1978 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173970 | |
| dc.subject | Complex Variables | |
| dc.subject | 32L10; 32C35; 13C15 | |
| dc.title | Homomorphisms of infinitely generated analytic sheaves | |
| dc.type | text |