  Quillen proved that repeated multiplication of the standard sesquilinear form
to a positive Hermitian bihomogeneous polynomial eventually results in a sum of
Hermitian squares, which was the first Hermitian analogue of Hilbert's
seventeenth problem in the nondegenerate case. Later Catlin-D'Angelo
generalized this positivstellensatz of Quillen to the case of Hermitian
algebraic functions on holomorphic line bundles over compact complex manifolds
by proving the eventual positivity of an associated integral operator. The
arguments of Catlin-D'Angelo, as well as that of a subsequent refinement by
Varolin, involve subtle asymptotic estimates of the Bergman kernel. In this
article, we give an elementary and geometric proof of the eventual positivity
of this integral operator, thereby yielding another proof of the corresponding
positivstellensatz.
