Hermitian analogues of Hilbert's 17-th problem

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.

to appear in Advances in Math

Cited by in corpus (1)

• Pfister's theorem fails in the Hermitian case