Abstract:Given a sequence ̺ = (r n ) n ∈ [0, 1) tending to 1, we consider the set U A (D, ̺) of Abel universal series consisting of holomorphic functions f in the open unit disc D such that for any compact set K included in the unit circle T, different from T, the set {z →. We prove that it does not coincide with any other classical sets of universal holomorphic functions. In particular, it not even comparable in terms of inclusion to the set of holomorphic functions whose Taylor polynomials at 0 are dense in C(K) for … Show more
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