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Positive polynomials on compact sets

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Abstract:

The aim of this note is to give short algebraic proofs of theorems of Handelman, Pólya and Schmüdgen concerning the algebraic structure of polynomials being positive on certain subsets of ℝn. The main ingredient of the proofs is the representation theorem of Kadison–Dubois. The proof of the latter is elementary and algebraic but tricky.

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Dortmund, 44221 Dortmund, Germany.¶e-mail: berr@mathematik.uni-dortmund.de, , , , , , DE

    Ralph Berr

  2. GAD, Weseler Straße 500, 48163 Münster, Germany.¶e-mail: twoermann@web.de, , , , , , DE

    Thorsten Wörmann

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  1. Ralph Berr
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  2. Thorsten Wörmann
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Received: 6 February 1999 / Revised version: 28 August 2000

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Berr, R., Wörmann, T. Positive polynomials on compact sets. manuscripta math. 104, 135–143 (2001). https://doi.org/10.1007/PL00005867

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  • DOI: https://doi.org/10.1007/PL00005867

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