论文标题
几乎到处都是近似身份的规范融合以及三角和Vilenkin系统的Fejér手段
Almost everywhere and norm convergence of Approximate Identity and Fejér means of trigonometric and Vilenkin systems
论文作者
论文摘要
在本文中，我们研究了具有特殊属性的非常通用的近似内核，称为近似身份，几乎在任何地方都证明了这些一般方法的范围，该方法由一类总结性方法组成，并提供了规范和A.E.这些总结性方法相对于三角系统的收敛性。对这些总结的研究也可用于获得有关Vilenkin系统的Fejér均值收敛，但这些方法对于研究A.E.并不有用。在这种情况下，由于fejér的内核的某些特殊特性，收敛。尽管存在这些不同的属性，我们还是提供了替代方法，以证明Fejér的融合几乎在Vilenkin Systems中的融合。
In this paper, we investigate very general approximation kernels with special properties, called an approximate identity, and prove almost everywhere and norm convergence of these general methods, which consists of a class of summability methods and provide norm and a.e. convergence of these summability methods with respect to the trigonometric system. Investigations of these summations can be used to obtain norm convergence of Fejér means with respect to the Vilenkin system also, but these methods are not useful to study a.e. convergence in this case, because of some special properties of the kernels of Fejér means. Despite these different properties we give alternative methods to prove almost everywhere convergence of Fejér means with respect to the Vilenkin systems.
