The Whitney extension problem and Lipschitz selections of set-valued mappings in jet-spaces
| dc.creator | Shvartsman, Pavel | |
| dc.date | 2006-01-29 | |
| dc.date.accessioned | 2026-07-07T06:59:26Z | |
| dc.date.available | 2026-07-07T06:59:26Z | |
| dc.description | We study a variant of the Whitney extension problem for the space $C^{k,ω}(R^n)$. We identify this space with a space of Lipschitz mappings from $R^n$ into the space $P_k \times R^n$ of polynomial fields on $R^n$ equipped with a certain metric. This identification allows us to reformulate the Whitney problem for $C^{k,ω}(R^n)$ as a Lipschitz selection problem for set-valued mappings into a certain family of subsets of $P_k \times R^n$. We prove a Helly-type criterion for the existence of Lipschitz selections for such set-valued mappings defined on finite sets. With the help of this criterion, we improve estimates for finiteness numbers in finiteness theorems for $C^{k,ω}(R^n)$ due to C. Fefferman. | |
| dc.identifier | https://arxiv.org/abs/math/0601711 | |
| dc.identifier | http://arxiv.org/abs/math/0601711 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107748 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46E35, 52A35, 54C60, 54C65 | |
| dc.title | The Whitney extension problem and Lipschitz selections of set-valued mappings in jet-spaces | |
| dc.type | text |