A Positivstellensatz which Preserves the Coupling Pattern of Variables
| dc.creator | Lasserre, Jean B. | |
| dc.date | 2006-09-19 | |
| dc.date.accessioned | 2026-07-07T07:24:58Z | |
| dc.date.available | 2026-07-07T07:24:58Z | |
| dc.description | We specialize Schmüdgen's Positivstellensatz and its Putinar and Jacobi and Prestel refinement, to the case of a polynomial $f\in R[X,Y]+R[Y,Z]$, positive on a compact basic semi algebraic set $K$ described by polynomials in $R[X,Y]$ and $R[Y,Z]$ only, or in $R[X]$ and $R[Y,Z]$ only (i.e. $K$ is a cartesian product). In particular, we show that the preordering $P(g,h)$ (resp. quadratic module $Q(g,h)$) generated by the polynomials $\{g_j\}\subset R[X,Y]$ and $\{h_k\}\subset R[Y,Z]$ that describe $K$, is replaced with $P(g)+P(h)$ (resp. $Q(g)+Q(h)$), so that the absence of coupling between $X$ and $Z$ is also preserved in the representation. A similar result applies with Krivine's Positivstellensatz involving the cone generated by $\{g_j,h_k\}$. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0609529 | |
| dc.identifier | http://arxiv.org/abs/math/0609529 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116569 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Optimization and Control | |
| dc.subject | Probability | |
| dc.subject | 14P10; 30C10; 90C22; 90C25 | |
| dc.title | A Positivstellensatz which Preserves the Coupling Pattern of Variables | |
| dc.type | text |