Local algebra bundles and $α$-jets of mappings
We present the functor associated with a local algebra bundle and the differential structure of the double fibre bundle it produces when applied to a differential manifold.
math.AC↗
arXiv subjects
Fiorella Barone
Publications and source records attributed to Fiorella Barone.
The category of local algebras and points proches
Categorial methods for generating new local algebras from old ones are presented. A direct proof of the differential structure of the prolongations of a manifold is proposed.
math.CT↗
Polarizations and differential calculus in affine spaces
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.
math.CA↗