Kohomologie mit Schranken und Fortsetzung holomorpher Funktionen durch lineare stetige Operatoren
| dc.creator | Schmitt, M. Matthias | |
| dc.date | 2002-02-25 | |
| dc.date.accessioned | 2026-07-07T04:46:41Z | |
| dc.date.available | 2026-07-07T04:46:41Z | |
| dc.description | In this thesis we solve the coboundary equation $δc=d$ with bounds for cochains with values in a coherent subsheaf of some $\mathcal{O}^p_Ω$, where $Ω$ is a Stein manifold. In particular the existence of a finite set of global generators is not assumed. Our result applies therefore to the ideal sheaf $\mathcal{J}_V\subset \mathcal{O}_{\C^N}$ of germs of holomorphic functions vanishing on a closed analytic submanifold $V\subset\C^N$. Although we are mainly interested in the estimates for the solutions of $δc=d$, the techniques used also lead to a proof for the classical Theorem B of Cartan for coherent subsheafs of some $\mathcal{O}^p_Ω$, avoiding the Mittag-Leffler argument. We derive an extension theorem for holomorphic functions on V to entire functions, with control on growth behaviour. \newline As a corollary we construct a linear tame extension operator $H(V)\to H(\C^N)$ under the hypothesis that H(V) is linear tamely isomorphic to the infinite type power series space $Λ_\infty(k^{\frac{1}{n}})$, n= dim$_{\C}V$; this condition is also necessary. Here the supnorms on H(V) are taken over intersections of V with polycylinders of polyradii e^m, $m\in \N$. Aytuna asked how much, and what kind of, information about the complex analytic structure of V is carried by the Fréchet space H(V). We prove that H(V) is linear tamely isomorphic to a power series space of infinite type if and only if V is algebraic. | |
| dc.description | 104 pages | |
| dc.identifier | https://arxiv.org/abs/math/0202263 | |
| dc.identifier | http://arxiv.org/abs/math/0202263 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63429 | |
| dc.subject | Functional Analysis | |
| dc.subject | Complex Variables | |
| dc.subject | 46M18 (primary); 32D15, 46E10 (secondary) | |
| dc.title | Kohomologie mit Schranken und Fortsetzung holomorpher Funktionen durch lineare stetige Operatoren | |
| dc.type | text |