Walsh-Nörlund平均的子序列的几乎处处收敛性
Almost everywhere convergence of subsequences of Walsh-Nörlund means
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中文总结 AI 辅助
本文研究Walsh-Nörlund平均的子序列收敛性，在Walsh-Paley系统的Nörlund平均上，采用更弱条件证明了L₁(G)中函数的对应平均几乎处处收敛到原函数。
中文摘要 AI 辅助
设{q_k:k∈ℕ}为非递增且凸的非负数列，满足q₀>0。本文主要结果是：对Walsh-Paley系统上由数列q定义的Nörlund平均，取多个正整数子序列{aₙ:n∈ℙ}，可证明当n→∞时，L₁(G)中的函数f对应的t_{aₙ}(f)几乎处处收敛到f，且所用条件比已知结果更弱。
英文摘要
Let $\{q_{k}: k\in\mathbb{N}\}$ be a non-increasing and convex sequence of non-negative numbers such that $q_{0}>0$. Our main result is to prove almost everywhere convergence \[ t_{a_{n}}(f)\to f \] of $f\in L_{1}(G)$ as $n\to\infty$, using several $\{a_{n}: n\in\mathbb{P}\}$ subsequences of positive integers for Nörlund means (defined by sequence $q$) on the Walsh-Paley system with weaker conditions than it was known before.
