Sums of squares of regular functions on real algebraic varieties

By Claus Scheiderer. 2000

147 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5d18138d796ba97ec9245c98a8e11678dab49388

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In Algebra and Number Theory

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Distinguished representations of non-negative polynomials (2005, background): “If f is only assumed to be non-negative on K, there is a local-global criterion for the existence of an identity (∗) [13].”
Optimality conditions and finite convergence of Lasserre’s hierarchy (2012, background): “6.1 of Scheiderer [27], because (0 , 0 , 1) is a zero f lying in the interior of the feasible set and f is a nonnegative but non-SOS form in ( x 1 , x 2 , x 3 − 1). of The ﬂat truncation condition is typically not satisﬁed for dual optimizers (1.2).”
Sums of squares on real algebraic surfaces (2006, background): “This is true regardless of the compactness of K [10].”
The moment problem for non-compact semialgebraic sets (2001, background): “Applying results from [19], they deduce from this that the fi do not solve the moment problem for nX 2, in the same way that we do.”
Positivity, sums of squares and the multi-dimensional moment problem II ⁄ (2005, methodology): “In the “Added to proof” at the end of [9], Scheiderer reports the discovery of a smooth compact surface KS with T alg S = TS .”
On the moment problem of closed semi-algebraic sets (2002, background): “ C[x] such that L(Tf(λ)) ≥ 0 annihilates the vanishing ideal of the real algebraic variety Kf(λ) = Cλ,λ∈ Λ. Therefore, by Theorems 3.11 and 3.12 in [PS] (which are essentially based on the results in [S]), the assumptions on Cλ imply that the sequence f(λ) has property (SMP) for any λ∈ Λ. Hence f ha”
Sums of squares on real algebraic curves (2003, background): “The same basic question was studied in [15] already, and so the present paper is a sequel to [15].”
An analogue of the Riesz–Haviland theorem for the truncated moment problem (2008, background): “For other results related to [42], see [26,33,39,40], and the references cited therein.”
On Hilbert's construction of positive polynomials (2007, unknown): “A G ] 1 4 Ju l 2 00 7”