This is an announcement for the paper "Representation and approximation of positivity preservers" by Tim Netzer.
Abstract: We consider a closed set S in R^n and a linear operator \Phi on the polynomial algebra R[X_1,...,X_n] that preserves nonnegative polynomials, in the following sense: if f\geq 0 on S, then \Phi(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.
Archive classification: math.FA math.RA
Mathematics Subject Classification: 12E05; 15A04; 47B38; 44A60; 31B10; 41A36
Remarks: 17 pages
The source file(s), positivitypreservers.tex: 49618 bytes, is(are) stored in gzipped form as 0902.0279.gz with size 15kb. The corresponding postcript file has gzipped size 99kb.
Submitted from: tim.netzer@gmx.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0902.0279
or
http://arXiv.org/abs/0902.0279
or by email in unzipped form by transmitting an empty message with subject line
uget 0902.0279
or in gzipped form by using subject line
get 0902.0279
to: math@arXiv.org.