论文标题
卷积不变的线性功能和应用程序的应用
Convolution invariant linear functionals and applications to summability methods
论文作者
论文摘要
我们在$ l^{\ infty}（\ mathbb {r}）$上研究拓扑上不变的均值，这是实际线上所有本质上有限制的函数的集合，并证明相对于单个卷积操作员的不变性就足以使态度不变。我们还将此结果的某些应用考虑到可总结方法。特别是，在$ l^{\ infty}（\ Mathbb {r}）$中引入了几乎收敛的概念，并获得了有关几乎收敛的tauberian定理，并获得了Wiener内核定义的可总结方法。此外，对于由Hölder总结方法定义的$ c _ {\ infty} $总结方法，我们为给定功能提供了必要和充分的条件，即可为$ c _ {\ infty} $汇总。
We study topologically invariant means on $L^{\infty}(\mathbb{R})$, the set of all essentially bounded functions on the real line, and prove that invariance with respect to a single convolution operator is sufficient for a mean to be topologically invariant. We also consider some applications of this result to summability methods. In particular, the notion of almost convergence is introduced for a function in $L^{\infty}(\mathbb{R})$, and a Tauberian theorem concerning almost convergence and a summability method defined by a Wiener kernel is obtained. Further, for the $C_{\infty}$ summability method, which is defined by the limit of Hölder summability methods, we provide a necessary and sufficient condition for a given function to be $C_{\infty}$ summable.
