Abstract: The Green function has a higher dimensional version called the pluricomplex Green function. The Siciak-Zakharjuta theorem states that the pluricomplex Green function is equal to the Siciak function, which is written in terms of polynomials. The usual grading of polynomials is the smallest dilate of the unit simplex containing its support. If the unit simplex is replaced by any compact convex set, a new grading of polynomials arises and a new Siciak function. We study when a generalization of the Siciak-Zakharjuta theorem applies in this setting.
