Power series — the structure of H.–O.–gaps

Abstract. Suppose that a power series \(f(z) = \sum_{\nu=0}^\infty a_\nu (z-z_0)^\nu\) with positive radius of convergence has a sequence of H.-O.-gaps. Then there exists a neighborhood \(U(z_0)\) of \(z_0\), such that the rearrangement \(f(z) = \sum_{\nu=0}^\infty b_\nu (z-\zeta)^\nu\) also has H.-O.-gaps for all \(\zeta\in U(z_0)\).