The Runge approximation theorem for generalized polynomial hulls
| dc.creator | Alaoui, Youssef | |
| dc.creator | Saad, My Abdelhakim El Idrissi | |
| dc.date | 2001-01-22 | |
| dc.date.accessioned | 2026-07-07T04:39:45Z | |
| dc.date.available | 2026-07-07T04:39:45Z | |
| dc.description | It is known from the Runge approximation theorem that every function which is holomorphic in a neighborhood of a compact polynomially convex set $K\subset \complexes^{n}$ can be approximated uniformly on $K$ by analytic polynomials. We shall here prove the same result when the role of the polynomially convex hull $\hat {K}$ is played by the generalized polynomial hull $h_{q}(K)$ introduced by Basener and which can be defined, for each integer $q\in {0,...,n-1}$, by $h_{q}(K)=\displaystyle\bigcup_{P\in \complexes [z_{1},...,z_{n}]} A_{P}$ where $A_{P}=\{z\in \complexes^{n}: |P(z)|\leq δ_{K}(P,z)\}$, and where $δ_{K}(P,z)$ denotes the lowest value of $||P||_{K\cap f^{-1}(0)}$ when $f$ ranges in the set of holomorphic polynomial maps $\complexes^{n}\to \complexes^{q}$ vanishing at $z$. | |
| dc.description | 5 pages, no figures, latex | |
| dc.identifier | https://arxiv.org/abs/math/0101175 | |
| dc.identifier | http://arxiv.org/abs/math/0101175 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60792 | |
| dc.subject | Complex Variables | |
| dc.subject | 32E20; 32E30 | |
| dc.title | The Runge approximation theorem for generalized polynomial hulls | |
| dc.type | text |