Generic Behavior of Classes of Taylor Series Outside the Unit Disk



It is known that, generically, Taylor series of functions holomorphic in the unit disk turn out to be “maximally divergent” outside of the disk. For functions in classical Banach spaces of holomorphic functions, as for example, Hardy spaces or the disk algebra, the situation is more delicate. In this paper, it is shown that the behavior of the partial sums on sets outside the open unit disk sensitively depends on the way the sets touch the unit circle. As main tools, results on simultaneous approximation by polynomials are proved.


Hardy spaces Disk algebra Universal functions 

Mathematics Subject Classification

30K05 (primary) 30B30 30H10 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • George Costakis
    • 1
  • Andreas Jung
    • 2
  • Jürgen Müller
    • 2
  1. 1.Department of Mathematics and Applied MathematicsUniversity of CreteHeraklionGreece
  2. 2.FB IV, MathematicsUniversity of TrierTrierGermany

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