Abstract
The main results concern the structure of divergence sets of power series on the unit circle. A class of setsF 1,F 1⊂F σ, is characterized which are not divergence sets for power series on the unit circle. It is also emphasized that, the divergence sets of power series can be of sufficiently complicated structure. Divergence sets of power series on the unit circle are studied, whose partial sums satisfy lim sup ¦s n(x)¦<∞ outside a set of first category. Analogous results hold for trigonometric series on [0,2π] and also for series with respect to Vilenkin sets on corresponding zero measure compact Abelian groups. Nonsummability sets for Abel's method on the unit circle are also studied for power and trigonometric series.
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