  Hermitian algebraic functions were introduced by Catlin and D'Angelo under
the name of "globalizable metrics". Catlin and D'Angelo proved that any
Hermitian algebraic function without non-trivial zeros is a quotient of squared
norms, thus giving an answer to a Hermitian analogue of Hilbert's 17th problem
in the non-degenerate case. The result was independently proved somewhat
earlier by D. Quillen in a special case, and using different methods.
  In this paper, we characterize all Hermitian algebraic functions that are
quotients of squared norms.
