Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9493438 | Journal of Algebra | 2005 | 16 Pages |
Abstract
Let g1,â¦,grâR[x1,â¦,xn] such that the set K={g1⩾0,â¦,gr⩾0} in Rn is compact. We study the problem of representing polynomials f with f|K⩾0 in the form f=s0+s1g1+â¯+srgr with sums of squares si, with particular emphasis on the case where f has zeros in K. Assuming that the quadratic module of all such sums is archimedean, we establish a local-global condition for f to have such a representation, vis-à -vis the zero set of f in K. This criterion is most useful when f has only finitely many zeros in K. We present a number of concrete situations where this result can be applied. As another application we solve an open problem from [S. Kuhlmann et al., Positivity, sums of squares and the multi-dimensional moment problem II, Adv. Geometry, in press] on one-dimensional quadratic modules.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Claus Scheiderer,