English

Hermitian analogues of Hilbert's 17-th problem

Complex Variables 2010-12-14 v1

Abstract

We pose and discuss several Hermitian analogues of Hilbert's 1717-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.

Keywords

Cite

@article{arxiv.1012.2479,
  title  = {Hermitian analogues of Hilbert's 17-th problem},
  author = {John P. D'Angelo},
  journal= {arXiv preprint arXiv:1012.2479},
  year   = {2010}
}

Comments

to appear in Advances in Math

R2 v1 2026-06-21T16:57:06.904Z