A quantified Tauberian theorem for sequences

作者：Seifert David^*

来源：Studia Mathematica, 2015, 227(2): 183-192.

DOI：10.4064/sm227-2-7

• Ingham's theorem
• Tauberian theorem
• sequences
• quantified
• rates of decay
• Katznelson Tzafriri theorem

The main result of this paper is a quantified version of Ingham's Tauberian theorem for bounded vector-valued sequences rather than functions. It gives an estimate on the rate of decay of such a sequence in terms of the behaviour of a certain boundary function, with the quality of the estimate depending on the degree of smoothness this boundary function is assumed to possess. The result is then used to give a new proof of the quantified Katznelson Tzafriri theorem recently obtained by the author (2014).

• 出版日期2015