Non-existence of degree bounds for weighted sums of squares representations |
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| Authors: | Claus Scheiderer |
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| Affiliation: | Fachbereich Mathematik und Statistik, Universität Konstanz, 78457 Konstanz, Germany |
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| Abstract: | Given a fixed family of polynomials , we study the problem of representing polynomials in the form | with sums of squares si. Let M be the cone of all f which admit such a representation. The problem is said to be stable if there exists a function such that every fM has a representation (*) with deg(si)(deg(f)). The main result says that if the subset K={h10,…,hr0} of has dimension 2 and the sequence h1,…,hr has the moment property (MP), then the problem is not stable. In particular, this includes the case where K is compact, dim(K)2 and the cone M is multiplicatively closed.
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| Keywords: | Non-negative polynomials Sums of squares Complexity Moment problem Real algebraic geometry |
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