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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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Volume 16, Issue 4


Positive polynomials on nondegenerate basic semi-algebraic sets

Huy-Vui Ha / Toan Minh Ho
Published Online: 2016-10-13 | DOI: https://doi.org/10.1515/advgeom-2016-0017


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


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About the article

Received: 2012-11-02

Revised: 2015-08-19

Revised: 2016-02-23

Published Online: 2016-10-13

Published in Print: 2016-10-01

Citation Information: Advances in Geometry, Volume 16, Issue 4, Pages 497–510, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2016-0017.

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