分组有界变差与几乎单调递减的关系

Relationship between Grouped Bound Variation and Almost Monotonic Decreasing

在Fourier分析中,对一些经典定理单调性的推广很有意义。探讨了分组有界变差与几乎单调递减之间的关系;利用数列本身特性,采用构造的方法,给出平凡的数列,并结合三角级数的一致收敛性等相关定理,构造更具有实用价值的数列证明了两者的互不包含关系。

In Fourier analysis, it is of great significance for the popularization of monotonicity of some classic theorems. This paper discusses the relationship between group bounded variation and almost monotonic decreasing. It makes use of characteristic of series, and adopts construction method to give ordinary series. In addition, it combines with uniform convergence and other relevant theorems of trigonometric series to construct the series with more practical value so as to prove mutual exclusive relationship between them.