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Positive polynomials on nondegenerate basic semi-algebraic sets

  • Huy-Vui Ha und Toan Minh Ho EMAIL logo
Veröffentlicht/Copyright: 13. Oktober 2016
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Advances in Geometry
Aus der Zeitschrift Advances in Geometry Band 16 Heft 4

Abstract

A concept of nondegenerate basic closed semi-algebraic sets in ℝn is introduced. These are unbounded closed semi-algebraic sets for which we obtain some representations of polynomials with positive infima (the polynomials are further assumed to be bounded if n>2) and solutions of the moment problem. The key to obtain these results is an explicit description of the algebra of bounded polynomials on a nondegenerate basic semi-algebraic set via the combinatorial information of the Newton polyhedron corresponding to the generators of the semi-algebraic set.

Keywords: Sum of squares; Positivstellensatz; Nichtnegativstellensatz; moment problem
MSC 2010: Primary 14P99; 44A60; Secondary 12E05; 12D15

Communicated by: C. Scheiderer

acknowledgement

We would like to thank the referee for the useful comments. This paper has been written while the authors were visiting the Vietnam Institute for Advanced Study in Mathematics (VIASM), Hanoi, Vietnam. The authors would also like to thank the members in our group for their comments.

Funding

Research partially supported by NAFOSTED, Vietnam, Grant No. 101.04.2014.40, 101.04-2014.23.

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Received: 2012-11-2
Revised: 2015-8-19
Revised: 2016-2-23
Published Online: 2016-10-13
Published in Print: 2016-10-1

© 2016 by Walter de Gruyter Berlin/Boston

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https://doi.org/10.1515/advgeom-2016-0017
Schlagwörter für diesen Artikel
Sum of squares; Positivstellensatz; Nichtnegativstellensatz; moment problem

Artikel in diesem Heft

  1. Research Article
  2. Comparison theorems on smooth metric measure spaces with boundary
  3. Research Article
  4. Hilbert schemes of some threefold scrolls over 𝔽e
  5. Research Article
  6. On caustics by reflection of algebraic surfaces
  7. Research Article
  8. Optimal cover of a disk with three smaller congruent disks
  9. Research Article
  10. Balanced and absorbing subsets with empty interior
  11. Research Article
  12. Hyperovals arising from a Singer group action on H(3,q2), q even
  13. Research Article
  14. A fixed point theorem in Euclidean buildings
  15. Research Article
  16. Positive polynomials on nondegenerate basic semi-algebraic sets
  17. Research Article
  18. Edges versus circuits: a hierarchy of diameters in polyhedra
  19. Research Article
  20. Monads for framed sheaves on Hirzebruch surfaces, Adv. Geom. 15 (2015), 55–76
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