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Positivity in power series rings. (English) Zbl 1183.13033

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.

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
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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
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[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
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