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 -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.
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