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- Publisher
- Springer Journals
- Copyright
- Copyright © 2009 by Springer-Verlag
- Subject
- Mathematics; Mathematics, general
- ISSN
- 0025-5874
- eISSN
- 1432-1823
- DOI
- 10.1007/s00209-009-0541-8
- Publisher site
- See Article on Publisher Site
Abstract
We ask whether every polynomial function that is non-negative on a real algebraic curve can be expressed as a sum of squares in the coordinate ring. Scheiderer has classified all irreducible curves for which this is the case. For reducible curves, we show how the answer depends on the configuration of the irreducible components and give complete necessary and sufficient conditions. We also prove partial results in the more general case of finitely generated preorderings and discuss applications to the moment problem for semialgebraic sets.
Journal
Mathematische Zeitschrift – Springer Journals
Published: Apr 28, 2009