Hermitian analogues of Hilbert's 17-th problem

2010/12/11 by John P. D’Angelo, John P. D'Angelo, D'Angelo, John P. · 1 citation
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Holomorphic and Operator Theory #Mathematics and Applications #math.CV

paper · pdf · doi:10.48550/arxiv.1012.2479

to appear in Advances in Math

arxiv created 2010/12/11 · openalex publication_date 2010/12/11 · arxiv updated 2010/12/14 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We pose and discuss several Hermitian analogues of Hilbert's 17-th problem. We survey what is known, offer many explicit examples and some proofs, and give applications to CR geometry. We prove one new algebraic theorem: a non-negative Hermitian symmetric polynomial divides a nonzero squared norm if and only if it is a quotient of squared norms. We also discuss a new example of Putinar-Scheiderer.

Cited by

• Some results related to Macaulay's Theorem about Hilbert functions and applications

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