Generic boundary behaviour of Taylor series in Hardy and Bergman spaces

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• 作者：Hans-Peter Beise ; Jürgen Müller
• 关键词：Backward shift ; Mixing operator ; Universality
• 刊名：Mathematische Zeitschrift
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：284
• 期：3-4
• 页码：1185-1197
• 全文大小：454 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1823
• 卷排序：284

文摘

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.