We consider families of unitarizable highest weight modules (H-lambda)(lamb
da is an element of L) on a halfline L. All these modules can be realized a
s vector valued holomorphic functions on a bounded symmetric domain D, and
the polynomial functions form a dense subset of each module H-lambda, lambd
a is an element of L. In this paper we compare the norm of a fixed polynomi
al in two Hilbert spaces corresponding to two different parameters. As an a
pplication we obtain that for all lambda is an element of L the module of h
yperfunction vectors H-lambda(-infinity) can be realized as the space of al
l holomorphic functions on D.