Polarizations and differential calculus in affine spaces
| dc.creator | Barile, Margherita | |
| dc.creator | Barone, Fiorella | |
| dc.creator | Tulczyjew, Wlodzimierz M. | |
| dc.date | 2005-10-18 | |
| dc.date.accessioned | 2026-07-07T06:47:36Z | |
| dc.date.available | 2026-07-07T06:47:36Z | |
| dc.description | Within the framework of mappings between affine spaces, the notion of $n$-th polarization of a function will lead to an intrinsic characterization of polynomial functions. We prove that the characteristic features of derivations, such as linearity, iterability, Leibniz and chain rules, are shared -- at the finite level -- by the polarization operators. We give these results by means of explicit general formulae, which are valid at any order $n$, and are based on combinatorial identities. The infinitesimal limits of the $n$-th polarizations of a function will yield its $n$-th derivatives (without resorting to the usual recursive definition), and the above mentioned properties will be recovered directly in the limit. Polynomial functions will allow us to produce a coordinate free version of Taylor's formula. | |
| dc.identifier | https://arxiv.org/abs/math/0510368 | |
| dc.identifier | http://arxiv.org/abs/math/0510368 | |
| dc.identifier | Linear and Multilinear Algebra 55 (2007), 121-146 | |
| dc.identifier | doi:10.1080/03081080600643611 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103704 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Commutative Algebra | |
| dc.subject | 26C05; 05A10; 26B12; 47H60 | |
| dc.title | Polarizations and differential calculus in affine spaces | |
| dc.type | text |