Mathematics – Algebraic Geometry
Scientific paper
2008-07-28
Mathematics
Algebraic Geometry
18 pages, 6 figures
Scientific paper
A finitely generated quadratic module or preordering in the real polynomial ring is called stable, if it admits a certain degree bound on the sums of squares in the representation of polynomials. Stability, first defined explicitly by Powers and Scheiderer, is a very useful property. It often implies that the quadratic module is closed; furthermore it helps settling the Moment Problem, solves the Membership Problem for quadratic modules and allows applications of methods from optimization to represent nonnegative polynomials. We provide sufficient conditions for finitely generated quadratic modules in real polynomial rings of several variables to be stable. These conditions can be checked easily. For a certain class of semi-algebraic sets, we obtain that the nonexistence of bounded polynomials implies stability of every corresponding quadratic module. As stability often implies the non-solvability of the Moment Problem, this complements Schmuedgen's result which uses bounded polynomials to check the solvability of the Moment Problem by dimensional induction. We also use stability to generalize a result on the Invariant Moment Problem by Cimpric, Kuhlmann and Scheiderer.
No associations
LandOfFree
Stability of Quadratic Modules does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Stability of Quadratic Modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stability of Quadratic Modules will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-312906