Finding the Maximum Modulus of a Polynomial on the Polydisk Using a Generalization of Steckin's Lemma

This paper is a generalization of the work of J.J. Green in Calculating the maximum modulus of a polynomial using Steckin’s Lemma. This lemma is generalized to higher dimensions and is used in an algorithm to locate the absolute global max of a polynomial on the polydisk. How to apply this algorithm to the real sphere and the complex ball is also explained.