On tensorial representatives of infinitesimal jets of higher separated orders. (Sur les représentants tensoriels des jets infinitésimaux d’ordre séparé supérieur.) (French) Zbl 0840.58004

Let \(\mathbb{R}\) be the real line, let \(L^{\mathstrut}_n{}^{r_1+\cdots+ r_s}_{p_1+\cdots+ p_s}\) denote the space of infinitesimal jets with origin \((0,\dots, 0)\in \mathbb{R}^{p_1}\times\cdots\times \mathbb{R}^{p_s}\) and target \(0\in \mathbb{R}^n\), of possibly different orders \(r_1,\dots, r_s\) with respect to different factors \(\mathbb{R}^{p_1},\dots, \mathbb{R}^{p_s}\). Polynomial mappings \(\mathbb{R}^{p_1}\times\cdots \times \mathbb{R}^{p_s}\to \mathbb{R}^n\), obvious representatives of these jets, can be identified with elements of the graded tensor algebra over \(\mathbb{R}\). A description of \(L^{\mathstrut}_n{}^{r_1+\cdots+ r_s}_{p_1 + \cdots p_s}\) as a tensor space is the aim of this short note. These spaces are claimed to have an application in information systems theory.
Reviewer: M.Marvan (Opava)


58A20 Jets in global analysis