Abstract
The sphere S 2d-1 naturally embeds into the complex affine space ℂd simplify the known Striktpcsitivstellensätze, when the supports are resticted to semi-algebraic subsets of odd dimensional spheres. We also illustrate the subtleties involved in trying to control the number of squares in a Hermitian sum of squares.
AMS(MOS) subject classifications. Primary 14PI0, Secondary 32A 70
The first author was partially supported by the National Science Foundation grant DMS-0500765.
The second author was supported in part by the Institute for Mathematics and its Applications (Minneapolis) with funds provided by the National Science Foundation and by the NSF grant DMS-0701094.
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D’Angelo, J.P., Putinar, M. (2009). Polynomial Optimization on Odd-Dimensional Spheres. In: Putinar, M., Sullivant, S. (eds) Emerging Applications of Algebraic Geometry. The IMA Volumes in Mathematics and its Applications, vol 149. Springer, New York, NY. https://doi.org/10.1007/978-0-387-09686-5_1
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