Positive polynomials and sequential closures of quadratic modules

Author:
Tim Netzer

Journal:
Trans. Amer. Math. Soc. **362** (2010), 2619-2639

MSC (2000):
Primary 44A60, 14P10, 13J30; Secondary 11E25

DOI:
https://doi.org/10.1090/S0002-9947-09-05001-6

Published electronically:
December 14, 2009

MathSciNet review:
2584613

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a basic closed semi-algebraic set in and let be the corresponding preordering in . We examine for which polynomials there exist identities

*fibre-preorderings*, constructed from bounded polynomials. These fibre-preorderings are easier to deal with than the original preordering in general. For a large class of examples we are thus able to show that either

*every*polynomial that is nonnegative on admits such representations, or at least the polynomials from do. The results also hold in the more general setup of arbitrary commutative algebras and quadratic modules instead of preorderings.

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Additional Information

**Tim Netzer**

Affiliation:
Fakultät für Mathematik und Informatik, Universität Leipzig, PF 100920, 04009 Leipzig, Germany

Email:
tim.netzer@math.uni-leipzig.de

DOI:
https://doi.org/10.1090/S0002-9947-09-05001-6

Keywords:
Moment problems,
semi-algebraic sets,
real algebra,
positive polynomials and sum of squares

Received by editor(s):
July 21, 2008

Published electronically:
December 14, 2009

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.