Pfister’s theorem fails in the Hermitian case

DOI10.1090/S0002-9939-2011-10841-4zbMath1309.12001arXiv1010.3215OpenAlexW2076735196MaRDI QIDQ5389377

Jiří Lebl, John P. D'Angelo

Publication date: 26 April 2012

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.3215

zbMATH Keywords

sums of squaresHermitian formsHilbert's 17-th problemHermitian lengthHuang lemma

Mathematics Subject Classification ID

Real algebraic sets (14P05) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Hermitian, skew-Hermitian, and related matrices (15B57) CR manifolds as boundaries of domains (32V15)

Related Items (2)

HERMITIAN COMPLEXITY OF REAL POLYNOMIAL IDEALS ⋮ Effective geometric Hermitian positivstellensatz

Cites Work

• Hermitian analogues of Hilbert's 17-th problem
• Normal forms, Hermitian operators, and CR maps of spheres and hyperquadrics
• On a linearity problem for proper holomorphic maps between balls in complex spaces of different dimensions.
• Degree estimates for polynomials constant on a hyperplane
• On the representation of hermitian forms as sums of squares
• Zur Darstellung definiter Funktionen als Summe von Quadraten. (To the representation of definite functions as the sum of squares)
• COMPLEX VARIABLES ANALOGUES OF HILBERT'S SEVENTEENTH PROBLEM
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