On the convergence (upper boundness) of trigonometric series

摘要

Inthispaperweprovethatthecondition$$sum_{k=left[rac{n}{2}ight]}^{2n}rac{k^{r}lambda_{k}}{|n-k|+1}=o(1),left(=O(1)ight),$$for$r=0,1,2,dots,$isnecessaryfortheconvergenceofthe$r-th$derivativeofthe...