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

Kawaguchi, Michiaki

Tensor, New Ser. 55, No. 3, 297-300 (1994).

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)

MSC:

58A20

Jets in global analysis

Keywords:

jets of separated order