Boundary Behavior and Cesàro Means of Universal Taylor Series

Frédéric Bayart


We study boundary properties of universal Taylor series. We prove that if f is a universal Taylor series on the open unit disk, then there exists a residual subset G of the unit circle such that f is unbounded on all radii with endpoints in G. We also study the effect of summability methods on universal Taylor series. In particular, we show that a Taylor series is universal if and only if its Cesàro means are universal.

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Revista Matemática Complutense
ISSN-e 1988-2807

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