  A famous result of Siciak is how the Siciak-Zakharyuta functions, sometimes
called global extremal functions or pluricomplex Green functions with a pole at
infinity, of two sets relate to the Siciak-Zakharyuta function of their
cartesian product. In this paper Siciak's result is generalized to the setting
of Siciak-Zakharyuta functions with growth given by a compact convex set, along
with discussing why this generalization does not work in the weighted setting.
