On the divergence of polynomial interpolation in the complex plane

We extend the results in [1] and [2] from the divergence of Hermite-Fejer i nterpolation in the complex plane to the divergence of arbitrary polynomial interpolation in the complex plane. In particular, we prove the following theorem: Let Delta (n)= -1 less than or equal to t(1)((n)) < ... < t(n)((n) ) <1. Let phik((n)) be polynomials of arbitrary degree such that phi ((n))( k)(t(j)((n))) = delta (kj).Then the Lebesgue function Delta (n)(x) = Sigma (n)(j=1) \phi ((n))(j) (x)\ tends to infinity at every complex neighborhood of some point in [-1, 1].