Cimprič, Jaka; Kuhlmann, Salma; Marshall, Murray Positivity in power series rings. (English) Zbl 1183.13033 Adv. Geom. 10, No. 1, 135-143 (2010). Summary: We extend and generalize results of C. Scheiderer [Manuscr. Math. 119, No. 4, 395–410 (2006; Zbl 1120.14047)] on the representation of polynomials nonnegative on two-dimensional basic closed semialgebraic sets. Our extension covers some situations where the defining polynomials do not satisfy the transversality condition. Such situations arise naturally when one considers semialgebraic sets invariant under finite group actions. Cited in 2 Documents MSC: 13F25 Formal power series rings 14P10 Semialgebraic sets and related spaces 14L30 Group actions on varieties or schemes (quotients) 20G20 Linear algebraic groups over the reals, the complexes, the quaternions Citations:Zbl 1120.14047 PDFBibTeX XMLCite \textit{J. Cimprič} et al., Adv. Geom. 10, No. 1, 135--143 (2010; Zbl 1183.13033) Full Text: DOI arXiv References: [1] Bochnak J., Sup. 8 pp 353– (4) [2] DOI: 10.1090/S0002-9947-08-04588-1 · Zbl 1170.14041 · doi:10.1090/S0002-9947-08-04588-1 [3] DOI: 10.1007/s002080100264 · Zbl 1006.32008 · doi:10.1007/s002080100264 [4] DOI: 10.1090/S0002-9947-02-03075-1 · Zbl 1012.14019 · doi:10.1090/S0002-9947-02-03075-1 [5] DOI: 10.1515/advg.2005.5.4.583 · Zbl 1095.14055 · doi:10.1515/advg.2005.5.4.583 [6] DOI: 10.1090/S0002-9947-99-02522-2 · Zbl 0941.14024 · doi:10.1090/S0002-9947-99-02522-2 [7] DOI: 10.1007/s00209-003-0568-1 · Zbl 1056.14078 · doi:10.1007/s00209-003-0568-1 [8] DOI: 10.1007/s00229-006-0630-5 · Zbl 1120.14047 · doi:10.1007/s00229-006-0630-5 [9] DOI: 10.1007/BF01446568 · Zbl 0744.44008 · doi:10.1007/BF01446568 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.