论文标题
关于泰勒系列在加权迪里奇的空间中的nörlund总结性
On Nörlund summability of Taylor series in weighted Dirichlet spaces
论文作者
论文摘要
在本说明中，我们表明，如果确定nörlundoperator的序列是不确定性的，并且具有有限的上层生长速率，则可以加权的dirichlet空间中的泰勒级数（广义）nörlund总结。特别是，泰勒系列是所有$α> 1/2 $的nörlund总结，并且收敛速度为$ o（n^{ - 1/2}）$的顺序。不平等$α> 1/2 $很清晰。另一方面，如果Taylor系列是可总结的，并且确定序列的部分总和享有一定的生长条件，则确定序列的生长速率较低。对于均匀界限零界限的非侵蚀序列，得出了模拟结果。
In this note we show that the Taylor series of a function in a weighted Dirichlet space is (generalized) Nörlund summable, provided that the sequence determining the Nörlund operator is non-decreasing and has finite upper growth rate. In particular the Taylor series is Nörlund summable for all $α>1/2$, and the rate of convergence is of the order $O(n^{-1/2})$. The inequality $α>1/2$ is sharp. On the other hand if the Taylor series is Nörlund summable and the partial sums of the determining sequence enjoy a certain growth condition then the determining sequence has finite lower growth rate. An analogue result is derived for a non-increasing sequence that is uniformly bounded away from zero.
