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arXiv · 2103.16134

On the bad points of positive semidefinite polynomials

Olivier Benoist
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Abstract

A bad point of a positive semidefinite real polynomial f is a point at which a pole appears in all expressions of f as a sum of squares of rational functions. We show that quartic polynomials in three variables never have bad points. We give examples of positive semidefinite polynomials with a bad point at the origin, that are nevertheless sums of squares of formal power series, answering a question of Brumfiel. We also give an example of a positive semidefinite polynomial in three variables with a complex bad point that is not real, answering a question of Scheiderer.

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BibTeXRIS

Olivier Benoist. 2022-05-23. On the bad points of positive semidefinite polynomials. https://doi.org/10.1007/s00209-021-02804-9

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