Maximal Convergence and Interpolation on Unconnected Sets

A theorem of Grothmann states that interpolating polynomials to a holomorphic function on a compact set E is maximally convergent to f only if a subsequence of the interpolation points converges to the equilibrium distribution of E in the weak* sense. Grothmann’s proof applies only for connected sets E . The objective of this paper is to provide a new necessary condition for maximal convergence which is the crucial tool to prove Grothmann’s theorem for unconnected sets E .