Pfister's theorem fails in the Hermitian case

Abstract

We show that the Hermitian analogue of a famous result of Pfister fails. To do so we provide a Hermitian symmetric polynomial $r$ of total degree 2d such that any non-zero multiple of it cannot be written as a Hermitian sum of squares with fewer than $d+1$ squares.

7 pages, to appear in Proc. Amer. Math. Soc., improved exposition in the proof

References in corpus (3)

• Normal forms, Hermitian operators, and CR maps of spheres and hyperquadrics
• Hermitian symmetric polynomials and CR complexity
• Hermitian analogues of Hilbert's 17-th problem

Cited by in corpus (1)

• Signature pairs of positive polynomials