Faber series with Ostrowski gaps

Let G be a simply connected domain in the complex plane. For a function f holomorphic in G, Faber expansions with respect to appropriate compact subsets of G are considered. It is shown that if f has so-called Ostrowski gaps with respect to one such compact set, then certain subsequences of the partial sums with respect to different compact sets have an equiconvergence property. This implies that the Ostrowski gap structure is shared by all Faber expansions of f. Moreover, it is shown that the equiconvergence property has some implications for universal Faber series. Corresponding (known) results for Taylor series are obtained as special cases.