Banach Spaces of Universal Taylor Series in the Disc Algebra

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• 作者：Luis Bernal-González ; Andreas Jung ; Jürgen Müller
• 关键词：Mathematics Subject ClassificationPrimary 47A16 ; Secondary 15A03 ; 40A30 ; 42A16 ; 46E10
• 刊名：Integral Equations and Operator Theory
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：86
• 期：1
• 页码：1-11
• 全文大小：505 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8989
• 卷排序：86

文摘

It is proved that there are large vector spaces of functions in the disc algebra for which every nonzero member satisfies that, for many small subsets E of the unit circle \({\mathbb{T}}\), the restrictions to \({\mathbb{T}}\) of the partial sums of its Taylor series at the origin approximate any prescribed function on E. Moreover, it is shown that such sets necessarily have to be small in terms of porosity.