On the behaviour of power series in the absence of Hadamard-Ostrowski gaps

摘要

We show that the partial sums (Snf)n∈N of a power series f with radius of convergence one tend to ∞ in capacity on (arbitrarily large) compact subsets of the complement of the closed unit disk, if f does not have so-called Hadamard-Ostrowski gaps. Regarding a recent result of Gardiner, this covers a large class of functions f holomorphic in the unit disk.