论文标题
关于nörlund的几乎无处
On the almost everywhere and norm convergences of Nörlund means with respect to Vilenkin systems
论文作者
论文摘要
与傅立叶序列的经典理论不同，该理论处理函数为正弦波的分解不同，Vilenkin（Walsh）函数是矩形波。 Vilenkin-Fourier系列理论的发展受到了三角学系列经典理论的强烈影响，但也有很多差异。我的硕士论文的目的是讨论，发展和应用与现代谐波分析有关的迷人理论的最新发展。特别是，我们研究了Nörlund的手段，但仅在其系数为单调并证明Lebesgue和Vilenkin-Lebesgue点的情况下。由于几乎到处都是Lebesgue和Vilenkin-Lebesgue的点，对于任何可用功能，我们几乎在任何地方都能获得这种总结性方法的融合。
Unlike the classical theory of Fourier series which deals with decomposition of a function into sinusoidal waves the Vilenkin (Walsh) functions are rectangular waves. The development of the theory of Vilenkin-Fourier series has been strongly influenced by the classical theory of trigonometric series but there are a lot of differences also. The aim of my master thesis is to discuss, develop and apply the newest developments of this fascinating theory connected to modern harmonic analysis. In particular, we investigate Nörlund means but only in the case when their coefficients are monotone and prove convergence in Lebesgue and Vilenkin-Lebesgue points. Since almost everywhere points are Lebesgue and Vilenkin-Lebesgue points for any integrable functions we obtain almost everywhere convergence of such summability methods.
