Polynomial Optimization on Odd-Dimensional Spheres

  • John P. D’AngeloEmail author
  • Mihai Putinar
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 149)


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.

Key words

Positive polynomial Hermitian square unit sphere plurisubharmonic function Cauchy-Riemann manifold 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Mathematics DepartmentUniversity of CaliforniaSanta BarbaraUSA

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