Representation and Approximation of Positivity Preservers
| dc.creator | Netzer, Tim | |
| dc.date | 2009-02-02 | |
| dc.date.accessioned | 2026-07-07T12:36:59Z | |
| dc.date.available | 2026-07-07T12:36:59Z | |
| dc.description | We consider a closed set S in R^n and a linear operator Φon the polynomial algebra R[X_1,...,X_n] that preserves nonnegative polynomials, in the following sense: if f\geq 0 on S, then Φ(f)\geq 0 on S as well. We show that each such operator is given by integration with respect to a measure taking nonnegative functions as its values. This can be seen as a generalization of Haviland's Theorem, which concerns linear functionals on polynomial algebras. For compact sets S we use the result to show that any nonnegativity preserving operator is a pointwise limit of very simple nonnegativity preservers with finite dimensional range. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/0902.0279 | |
| dc.identifier | http://arxiv.org/abs/0902.0279 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/218284 | |
| dc.subject | Functional Analysis | |
| dc.subject | Rings and Algebras | |
| dc.subject | 12E05; 15A04; 47B38; 44A60; 31B10; 41A36 | |
| dc.title | Representation and Approximation of Positivity Preservers | |
| dc.type | text |