Blenders
Number Theory
2011-02-15 v2 Algebraic Geometry
Combinatorics
Abstract
A blender is a closed convex cone of real homogeneous polynomials that is also closed under linear changes of variable. Non-trivial blenders only occur in even degree. Examples include the cones of psd forms, sos forms, convex forms and sums of -th powers of forms of degree . We present some general properties of blenders and analyze the extremal elements of some specific blenders.
Keywords
Cite
@article{arxiv.1008.4533,
title = {Blenders},
author = {Bruce Reznick},
journal= {arXiv preprint arXiv:1008.4533},
year = {2011}
}
Comments
Revised version; will appear in "Notions of Positivity and the Geometry of Polynomials" (P. Branden, M. Passare, M. Putinar, editors), Trends in Math., Birkhauser, Basel