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Mathematische Zeitschrift

, Volume 284, Issue 3–4, pp 1185–1197 | Cite as

Generic boundary behaviour of Taylor series in Hardy and Bergman spaces

  • Hans-Peter Beise
  • Jürgen MüllerEmail author
Article

Abstract

It is known that, generically, Taylor series of functions holomorphic in the unit disc turn out to be universal series outside of the unit disc and in particular on the unit circle. Due to classical and recent results on the boundary behaviour of Taylor series, for functions in Hardy spaces and Bergman spaces the situation is drastically different. In this paper it is shown that in many respects these results are sharp in the sense that universality generically appears on maximal exceptional sets. As a main tool it is proved that the Taylor (backward) shift on certain Bergman spaces is mixing.

Keywords

Backward shift Mixing operator Universality 

Mathematics Subject Classification

30B30 30K05 47A16 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.FB IV, MathematicsUniversity of TrierTrierGermany

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