On the bad points of positive semidefinite polynomials - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Mathematische Zeitschrift Année : 2022

On the bad points of positive semidefinite polynomials

Résumé

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.

Dates et versions

hal-03906737 , version 1 (19-12-2022)

Identifiants

Citer

Olivier Benoist. On the bad points of positive semidefinite polynomials. Mathematische Zeitschrift, 2022, 300 (4), pp.3383-3403. ⟨10.1007/s00209-021-02804-9⟩. ⟨hal-03906737⟩
4 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More