Non-existence of degree bounds for weighted sums of squares representations

DOI10.1016/j.jco.2005.04.001zbMath1093.13024OpenAlexW2085951741MaRDI QIDQ2577530

Claus Scheiderer

Publication date: 22 December 2005

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jco.2005.04.001

zbMATH Keywords

complexitymoment problemreal algebraic geometrynon-negative polynomials

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Real algebraic and real-analytic geometry (14P99) Real algebra (13J30)

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Cites Work

• A remark on the multidimensional moment problem
• The \(K\)-moment problem for compact semi-algebraic sets
• An algorithm for sums of squares of real polynomials
• Solving moment problems by dimensional extension
• Sums of squares on real algebraic curves
• Distinguished representations of non-negative polynomials
• Complexity estimates for the Schmüdgen Positivstellensatz
• Distinguished representations of strictly positive polynomials
• The moment problem for non-compact semialgebraic sets
• Positivity, sums of squares and the multi-dimensional moment problem
• On the moment problem of closed semi-algebraic sets
• Sums of squares of regular functions on real algebraic varieties
• Positivity, sums of squares and the multi-dimensional moment problem II
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