Polynomial inequalities and universal Taylor series

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• 作者：Augustin Mouze ; Vincent Munnier
• 关键词：Universal series ; Frequently universal series ; Bernstein inequality ; Density
• 刊名：Mathematische Zeitschrift
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：284
• 期：3-4
• 页码：919-946
• 全文大小：619 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

We derive several new properties concerning both universal Taylor series and Fekete universal series from classical polynomial inequalities. In particular, we study some density properties of their approximating subsequences. Moreover we exhibit summability methods which preserve or imply the universality of Taylor series in the complex plane. Likewise we show that the partial sums of the Taylor expansion around zero of a \(C^{\infty }\) function is universal if and only if the sequence of its Cesàro means satisfies the same universal approximation property.