POLYNOMIAL HULLS OF GRAPHS

We shall consider the polynomially convex hull of the graph of a continuous complex-valued function on the boundary of the unit ball. We show first that the hull covers the closed unit ball and then consider several of its properties. In particular, when is the hull also a graph; i.e. single sheeted? When the hull is a graph we show, in some cases, that it contains analytic structure. We also consider the graph in C2 of a real-valued continuous function on the boundary of a 3-cell which is contained in a real hyperplane in C2 and partially extend some results of Bedford and Klingenberg who studied the case of smooth functions.